Caution: This runs long. The short version? The game doesn't say. Play how you want.
The special initiative action ready, in part, at first says, "The action [that the creature that took the action ready picked] occurs just before the action that triggers it," but then the description continues, saying, "If the triggered action is part of another character's activities, you interrupt the other character. Assuming he is still capable of doing so, he continues his actions once you complete your readied action" (Player's Handbook 160).
One issue is that The triggered action occurs before the triggering action and The triggering action interrupts the triggered action are kind of incompatible. That is, the game explains only how a handful of actions—like counterspelling and distracting a spellcaster—can interrupt an action. The game leaves the rest of the ready action for the DM to adjudicate, including the pregnant statement After the triggered action, if he can, the subject that triggered the actions continues his actions. (Even the Dungeon Master's Guide on Adjudicating the Ready Action (25–6) is little help!)
Another issue is that, to my knowledge, there's absolutely no good published example of how the ready action is intended to work except in that handful of specific instances described in the ready action itself. That is, there are combat examples in Sword and Fist, for instance, and in one a dude takes the ready action, but here's that example:
Druga anticipates a charge from Alarion, so both he and his warhorse prepare to attack Alarion’s mount when it approaches within range. Druga and his horse ready attack actions (Druga with his longsword, the warhorse with a hoof). (65 and italics preserved from the original)
That's it. And this example ain't like, for example, smashing an about-to-be-consumed potion. Likewise, the Web column Gamestoppers has folks take the special initiative action ready, but they only take it only so they can distract spellcasters. (It also doesn't help either that both sources of examples are for the unrevised dnd-3e game.)
Below are offered two of the schools of thought on the special initiative action ready. There are undoubtedly others, but these are the two that I've encountered most frequently in online forums. A DM should pick one or develop his own at a campaign's beginning lest fights ensue later on.
Approach #1: A creature can ready an action so that the subject wastes its action
When a creature takes the action ready and picks an action then picks a trigger like When a subject does
X, the creature takes the picked action when the subject's player says that the subject is going to do
X. That is, when a creature takes the action ready, everybody essentially adds a step to any actions he or she takes: instead of just doing
X, first, a creature claims it'll do
X, then, second, the creature actually does
X, and making the claim commits the subject to the action.
Thus, when a subject makes a claim that matches a creature's picked trigger, the trigger is pulled and the creature may take picked action. After the picked action is resolved, if the subject now can't do
X, then the subject loses that action.
Peake the bugbear chieftain takes a standard action to take the ready action, picking the action Attack the potion and the trigger When Nadir tries to drink the potion. On her turn, Nadir claims that she'll take a move action that provokes attacks of opportunity to retrieve an item—the potion—then takes that action. Then Nadir claims she'll take a standard action that provokes attacks of opportunity to drink the potion. Peake's trigger is pulled, Peake makes an attack roll against the potion (AC 10 + its size modifier + Nadir's Dexterity modifier) and succeeds, destroying the potion. Nadir, committed to the act of drinking the potion via her claim, loses her standard action.
If the DM just tells players when a creature takes the action ready and what the creature picked as a trigger, then claims needn't be formalized, but if the DM keeps the trigger secret, this DM recommends prevent arguments by formalizing claims.
My reading of forums leads me to believe that many folks—perhaps even the majority—adjudicate the ready action this way. (The exact phrasing will differ; I mean, I've never read elsewhere this process described exactly this way.) This method adjudication, essentially, adds a trading card game-style declare phase to the game when a creature takes the action ready, and the addition of this declare phase really does make the ready action far more playable and comprehensible.
Approach #2: Often a creature can ready an action so that the subject can't take that action, but the subject can still take a different action; however, some specific actions can be interrupted so that they're wasted
When a creature takes the action ready and picks an action then picks a trigger like When a subject does
X, the creature takes the picked action when the subject does
X. If the game has specific rules for interrupting
X, then those rules are used (e.g. casting a spell). If the game lacks rules for interrupting
X, the creature's picked action occurs before
X and, upon the resolution of the creature's picked action, the subject can do something else, the subject opting for a different action than the subject originally intended in light of changed battlefield conditions.
Yes, this is more than a little opaque and, beyond that, a little nuts, too, as it borders on, like, Schrödinger's action territory, but bear with me as I offer an example:
Peake the bugbear chieftain takes a standard action to take the ready action, picking the action Attack the potion and the trigger When Nadir drinks the potion. On her turn, Nadir drinks the potion. Peake's trigger is pulled, but there are no specific rules for interrupting drinking a potion, so Peake's picked action occurs before Nadir drinks the potion. Peake makes an attack roll against the potion (AC 10 + its size modifier + Nadir's Dexterity modifier) and succeeds, destroying the potion. It's still Nadir's turn, and Nadir's taken no actions—she didn't actually drink the potion! She takes a full-round action to make a full attack against Peake.
Until they wrap their heads around it—and sometimes even afterward—, this makes folks awfully uncomfortable. The theory goes like this: When a creature takes the action ready, it's establishing what it wants to do, but the creature has no control over the subject of the ready action. So when Peake took that ready action and in response to the picked trigger took the picked action, Peake only performed his action. While the subject may be—and, in this case, was—affected by it, the subject is free to adapt to it and change actions now that the battlefield has changed.
Why this makes folks uncomfortable should be clear, but just in case, let me state it: What folks tend to want to do is not just respond to a foe doing
X but both respond to the foe doing
X and prevent the foe from doing
X. Unfortunately, most of the game's actions don't have rules for both: for example, casting a spell does, but swinging a sword, drinking a potion, or even moving don't. Explaining this may initially result in exchanges like this:
Player: But Peake broke Nadir's potion when she went to drink it, so Nadir should lose her standard action.
DM: But Nadir never took that standard action to drink the potion; Peake took his action first, triggered by what would have been Nadir drinking the potion. Nadir totally would've drunk that potion had Peake not broken it, but, after resolving Peake's attack against the potion, it's still Nadir's turn, and she's taken no actions, so Nadir makes a full attack.
Player: So if Peake hadn't've broken the potion, Nadir would've taken a standard action to drink it, and Peake wouldn't be staring down Nadir's sword right now?
DM: That's accurate, yes. Peake can't know how someone will react to changing battlefield conditions. Peake only knows what he'll do.
This reading is built on a couple of different ideas. First, the rules don't mention the existence of a general claim step. (The special attack charge, for example, does have a claim step in which the creature picks the target of his charge; most events don't.) That is, folks typically really do just plunge ahead and do
X; only under specific circumstances—and the ready action isn't described as one of those circumstances—does the game require folks to first announce their intention to do
X then actually do
Second, a creature can't forfeit an action it didn't take. For example, Nadir didn't drink the potion; I mean, she totally would've but, ultimately, she didn't. Narrating this gets a little complicated, but comes down to the DM saying, "Had the creature's picked actions not prevented the subject from taking its action, the subject would've gone through with the action the creature prevented." That may seem a small consolation to the creature that's now on the receiving end of the subject's full attack, for example, but if the DM makes sure everybody understands that the special initiative action ready does not typically let the creature mandate the subject's actions but, instead, lets the creature control its own actions, things may go a little more smoothly. But, yes, in the end, this approach is much more difficult than just creating a claim phase.
Note: The second approach is tacitly endorsed (seriously, tilt your head and squint a lot) by the Dragon #315 Wizards Workshop column "Sage Advice: Combat and Casting: Official Answers" with the exchange beginning, "Suppose a fighter and an archer go at the same initiative.…" (109) and that's repeated almost verbatim by the Main FAQ (74). The Sage at the time is dnd-3e co-designer Skip Williams. This semiendorsement, of course, doesn't make the second approach any more playable.
"What about attacks of opportunity?"
Attacks of opportunity specifically and always interrupt the action that was taken:
An attack of opportunity “interrupts” the normal flow of actions in the round. If an attack of opportunity is provoked, immediately resolve the attack of opportunity, then continue with the next character’s turn (or complete the current turn, if the attack of opportunity was provoked in the midst of a character’s turn). (Player's Handbook 137)
Nobody knows what this means either because the same problem with attacks of opportunity exist with the special initiative action ready: the game is mostly silent on what happens if the interruption should prevent an action that a creature's presumably in the middle of!
This reader suspects most folks use a Magic: The Gathering-style last-in-first-out (LIFO) stack that sees the final attack of opportunity in a cascade happen first then the next-to-last and successively earlier ones occur in order approaching the original event. Then, if at any point a creature is unable to complete an action, the cascade ends and the LIFO stack is cleared. Here once more is the question's example, absent any resolutions:
Peake takes a standard action to make a sunder attempt against Nadir's rapier. Peake doesn't have anything special to help with sunder attempts, so Peake provokes an attack of opportunity from Nadir by making a Sunder attempt. Nadir makes the attack of opportunity and opts to make a disarm attempt against Peake. Nadir doesn't have anything special to help with disarm attempts, so Nadir provokes an attack of opportunity from Peake by making a disarm attempt.
To resolve this situation using the LIFO stack approach, Peake resolves his normal it'll-deal-damage attack of opportunity due to Nadir's disarm attempt first; if this kills her, the stack's cleared. If not, then Nadir resolves her disarm attack of opportunity due to Peake's sunder attempt next; if Nadir disarms Peake of his weapon that was used to make the sunder attempt, the stack's cleared. If not, then Peake makes his sunder attempt; when that resolves, the stack's cleared.
The alternative approach allows changing an action if it hasn't yet been taken. For example, a creature can, due to battlefield conditions changing, change its action as if it'd not taken the original action… because it hasn't yet taken that action! Changing an action in this way, however, doesn't obviate any of attacks of opportunity already provoked—those still occur—and, in fact, with the new action, the creature can provoke even more attacks of opportunity!
For example, once his weapon's at Nadir's feet, Peake, if his actions permit, could, instead of making the sunder attempt, take a move action to move up to his speed, and, if he leaves or moves within Nadir's threatened area normally, he'll provoke another attack of opportunity from Nadir. Again, like the second approach to readying an action, this may just feel wrong to players used to claims committing creatures to actions rather than actions committing creature to actions.
Once again, the DM should explain how things work in the campaign before the campaign's beginning lest players' expectations be violated during play.
Note: I'd not realized until after composing this answer that the Main FAQ endorses the LIFO approach by name in the Main FAQ in the exchange beginning, "Is it possible for an attack of opportunity to provoke an attack of opportunity?" (69-70). Unfortunately, my personal notes don't detail if this ruling has a provenance besides the Main FAQ itself.
It may interest some readers that Player's Option: Combat & Tactics (1995) for Advanced Dungeons & Dragons, 2nd Edition from which comes the attacks of opportunity concept has an attack of opportunity only and exclusively being a for-damage regular ol' melee attack—other kinds of attacks like disarm and trip had to be made on a creature's turn. Totally without proof and as utterly baseless speculation, this reader imagines that the phrase "or even as an attack of opportunity" was added at the very last minute to the Player's Handbook (2000) table Actions in Combat—and never actually playtested—by an enterprising editor thinking Meh… What harm could it do? and gamers have been paying the price ever since.