Teleporting Dryad

[Crake]

There may be some argument over whether the tree counts as an "object" or a "creature".

There is actually 0 argument over it. By dnd's own definition, to qualify as a creature you must have a wis and cha score, and you can't have one without the other. Wisdom being defined as the ability to percieve the world around you, and charisma (in it's most basic form) as the ability to differentiate yourself from not yourself. Without those two things (which trees do not have) you are an object. Objects CAN have other ability scores; I know certain objects are documented as having str and dex scores (notably various traps), and I imagine a tree would have a con score, though I've not ever heard of an object having an intelligence score WITHOUT also having a wis and cha score (intelligent items have all 3, and are actually considered constructs for resolving effects).

As for the main topic of this thread though: Ultimately, there's no real precedence for what your DM has done, so nobody can really give you clear ideas of how it would work. Since your DM is the one who made this ruling (which I and many others strongly disagree with), he would be the one who you should be asking these questions to, as even if we were to give you answers, that doesn't mean he will agree with them at all.