Started playing with 2 vessels at once, and some animations seem to be "over-animating"... most, if not all, animations with parents. Played around and PLB camera animations work fine, and they have parents. Turns out they don't declare MGROUP_XYZ as static, but instead use a pointer and allocate a new instance and use a function called AddManagedAnimationComponent() to deal with the memory at the end. A bit more digging and I found that it was added by SiameseCat back in 2009 with the log "Fixed animation bugs in multi-shuttle scenarios".
So it seems updating our animations to use AddManagedAnimationComponent() is the way to go if we want to have more than one instance of a vessel.
I'd like to use this opportunity to (perhaps) do more animation cleanup, but I got no answers on this question:
https://www.orbiter-forum.com/showthread.php?p=567581 :shrug: