The Binding spell has a potentially permanent duration and could have been used by Catherine to save herself from the calamity as described, with just three minor problems:
1) the binding spell is dismissable
2) the binding spell is not castable by a 13th level magic user (barely).
This can be solved by her having cleverly used a scroll of binding to dodge her imminent destruction, but that scroll having been cursed so as to not be dismissable (or maybe someone else cast the spell for her and then died. You have options). The method of binding should probably be minimus containment, with the vessel being the throne. A throne isn't really terribly container-like but it does sort of work, and maybe her incredibly tiny form could be seated upon it, if you're up for changes, otherwise it could just be too small to see.
When the party enters, she casts Magic Jar, and then keeps trying until she takes over somebody's body, trapping the person she swapped with in her doll-like/microscopic form. Her spells known should be something like:
Circle of Death
Summon Invisible Stalker (as Shambler, but 1 8HD Invisible Stalker instead, and you can exceed the one-week duration if you don't mind it killing you in your sleep. Basically, the Invisible Stalker spell from OD&D can be retained without issue as a 6th level spell. Some support for this idea can be found here, where someone left the spell as is when converting a 2e campaign to 3.5)
Contact Other Plane
To handle the extra spell, have Catherine's Crown Jewels (conveniently hidden within her throne) function as a Knowstone for one of these spells (est. value 25K gp, which is twice the original value of that hoard, unfortunately. Restrictions on usage to lower the value may be appropriate)
Haste, if you're okay with using the 3.0 version (i.e. extra action each turn) Otherwise replace it with something more useful for action economy manipulation, like Celerity + Quick Recovery feat, and take Dispel Magic as the third level slot, losing Detect Scrying
Nystul's Magic Aura
This conversion assumes that Sorcerer is a better fit for Princess Catherine, but you could make a conversion for a Wizard instead, which would be nearly identical except that, lacking a spellbook and material components, Catherine would be unable to cast most spells and unable to prepare any should she cast any. However, she would also possess a 7th level spell slot, and at least two 7th level spells, one of which should certainly be Drawmij's Instant Summons, and an additional gem in the secret compartment of the throne, among the Crown Jewels, should be a saphire worth at least 1000 gp which she can crush to retrieve her spellbook.
The sorcerer version, like the original, should magic jar into one of the party members, then 1d2ish rounds later TPK with Death Spell/Circle of Death. The new version needs to chain Magic Jar, though, in order to truly ecspe, so her new tactics go something like this:
Round 0: Magic Jar into one of the throne's decorations all sneaky like.
Round 1: Possess a PC. Keep trying till it works.
Round 2: Try to Magic Jar again, with a different cheap decorative gem. You might not be able to because bodies are weird. Keep trying til you do.
Round 3: Possess a different PC, while the others are freaking out about how one of them just suddenly died with no warning.
Round 4-end of combat: Kill 'em all! Show regard for personal safety only if you got a really sweet new body you actually like (female, similar ethnicity to Catherine's old body, right height, etc). Otherwise, if you die, you just grab a new body via the spell, which hasn't ended yet, returning to the 'dead' PC if the party succeeds on enough Will saves, and then just Magic Jar-ing again. You've got 6 5th level slots, so you get 6 times the number of PCs minus one attempts at getting a body you can keep before you have to start wasting 6th level slots that would be better spent on Circle of Death, or Invisible Stalker if the PCs are 10th level or higher.
When the party is incapacitated: If the party is incapacitated, bind helpless or kill any bodies connected to currently-trapped PC lifeforces, Then break the first Magic Jar gem after moving its body far enough away that doing this kills the PC, which ends the relationship between the binding body and that first body you took. Move the first body back into range afterwards. Then bind your current body helpless, and end the second Magic Jar, returning you to the unbound first body, and the second prisoner to the bound body you had been using. Do with the second prisoner whatever you want, and resume rulership of Castle Amber (and probably try to figure out who was responsible for the whole everyone-dying thing way back when, and maybe get a greater restoration to help with the PTSD).