What was probably discovered was not a wand holding the 7th-level Sor/Wiz spell simulacrum [illus] (Player's Handbook 279–80) because a typical wand only holds up to a 4th-level spell (q.v. the feat Craft Wand (93)). The creature probably found a new magic item like a staff of simulacrum (see Dungeon Master's Guide 214) or a typical scepter of simulacrum (Lost Empires of Faerûn 8).
Moreover, in this DM's campaign the creature would have found a staff of simulacrum (Mixcoatl the couatl) (7th-level spell at caster level 13) (358,250 gp or 7,165 gp plus masterwork quarterstaff; 4 lbs.) or a scepter of simulacrum (Xozgunnun the balor) (7th-level spell at caster level 13) (368,250 gp or 7,365 gp per charge; 2 lbs.). That is, rather than a staff of simulacrum or scepter of simulacrum that, for instance, can create a duplicate of any creature of up to a set number of Hit Dice, the discovered staff or scepter could instead only create duplicates of the indicated creature.
Finally, as can be seen by their prices, a creature that finds one of these items is lucky indeed. More valuable magic items can be created—a new staff of wish (max. 5,000 XP ea.) (9th-level spell at caster level 17) (1,364,750 gp or 27,295 gp per charge plus masterwork quarterstaff) or a scepter of forbiddance (password: rutabaga) (6th-level spell at caster level 11) (1,549,500 gp or 30,990 gp per charge; 2 lbs.), for example—, but a new staff or scepter of simulacrum is pretty high up there because each casting of the simulacrum spell costs at least 1,000 XP. So a dude probably doesn't make a scepter of simulacrum (Dalmosh of the Infinite Maws) (7th-level spell at caster level 13) (478,250 gp or 9,565 gp per charge; 2 lbs.) and, like, forgets it on the roof of his carriage. But, sure, let's say a creature discovers one anyway.
Do the game's rules prevent a creator from making use of a duplicate's abilities?
Once the duplicate's abilities are codified—and the question makes clear that any issues surrounding that topic have already been resolved—, according to the rules nothing seems to prevents the duplicate's creator from ordering the duplicate to use those abilities on the creator's behalf. By the same token, nothing normally prevents the duplicate from obeying its creator's orders.
The simulacrum spell says, "At all times the simulacrum remains under your [i.e. the creator's] absolute command. No special telepathic link exists, so command must be exercised in some other manner" (PH 279). Thus it seems that, normally, only by preventing the creator from issuing commands to the duplicate or by preventing the duplicate from receiving its creator's commands can the duplicate be prevented from using its abilities on the creator's behalf. (A creator's command isn't sufficient to allow the duplicate to break its own abilities rules, though. For instance, a duplicate of a trumpet archon can't use its teleport supernatural ability from its archon subtype to teleport with 51 lbs. of objects, no matter its creator's order.)
Does the game's lore prevent a creator from making use of a duplicate's abilities?
So far as I can tell, nothing in the game's lore generally prevents a creator from ordering a duplicate to use its abilities on the creator's behalf, and nothing in the game's lore generally prevents the duplicate from carrying out those orders. For example, no inevitable polices a natural law covering this. Nonetheless, the game's assumed lore is a fluid and volatile topic, varying in texture and intensity with the DM, the campaign, and the setting.
To illustrate, when the simulacrum spell creates a duplicate, this DM has always imagined the duplicate as an actual and identical duplicate except for exceptions imposed by the simulacrum spell. So in this DM's campaigns, the duplicate knows what the original knows, thinks like the original thinks, and feels about stuff the way the original feels about stuff. A duplicate still can't resist the orders of its creator—absolute command remains absolute command—, but the duplicate can totally not like following its creator's orders and, unless told not to, can plot against the creator, attack the creator, or just leave. This means the first orders issued to any duplicate should be Don't cover your ears then Stay here then Don't hurt me then Don't plot against me then Don't twist my orders—including these orders that I just gave you. (As can be seen, the first moments with a new duplicate are vitally important. Rule #1 of Simulacrum Club is Talk fast.)
So, yeah, once that's out of the way, if the creator of a duplicate of Mixcoatl the couatl orders the duplicate to plane shift the party to the Abyss so that the creator can cut deals with demons on their own turf, then if Mixcoatl the couatl would have a problem with that, so would its duplicate, but the duplicate still can't refuse its creator's order. (If the creator has not issued orders like those above to the duplicate, though, all best are off and hilarity could ensue!) This also means that if the campaign's couatls fight evil, then a duplicate will want to fight evil, and if the campaign's balors like to torture, then a duplicate will like to torture, and so on. Plus, even if the creator doesn't limit a duplicate's autonomy with an order like Only do exactly what I tell you to do, some percentage of folks will likely consider a creator's absolute command over the duplicate actual slavery. (And some folks will likely remain unmoved even after the creator explains that the duplicate is just an ice sculpture given life.)
Last and probably least, while many creatures like the couatl can assume a more innocuous form, other creatures like a balor, a trumpet archon, or Dalmosh can't. Thus, unless the creator conceals this association or additional resources are devoted to hiding this association, the creator will be publicly associated with the duplicate. In much the same way that the game's lore generally doesn't pass judgment on necromancy, in many settings it's at least frowned upon to exhume grandma, cast create undead on the corpse so that grandma's now a mummy, then go from town to town on adventures with that mummy. Likewise, even after explaining that the duplicate of Xozgunnun the balor is totally under his absolute command, a dude who adventures with a duplicate of a balor may not be welcome at the local church of Pelor.
This social component doesn't have a direct and immediate impact on the creator's secondhand use of the duplicate's abilities, but if the duplicate is of a kill-on-sight monster, folks'll try to kill it on sight, and if they're successful then the duplicate's destruction does prevent the creator from using its abilities! Just something to keep in mind.
Note: The Web adventure "The Thunder Below" (2004) by James Jacobs sees a stealth nerf to the simulacrum spell that, to the best of my knowledge, has never before and never again been mentioned canonically: "Since simulacrums have no memories in common with their source, though, their immediate usefulness as informants is limited" (9). Ask the DM if duplicates are tabula rasa as, if they are then a creator needn't worry as much about duplicates scheming against him.