Do you have a link to this magic item?
I'm not familiar with any rings of transmutation immunity. This sounds like a GM custom item, so its functioning would be completely up to him.
Personally, by its name, I feel such a ring would suppress any shape-changing effects and prevent any new transmutation school effects from taking hold. This would leave your doppleganger in its natural form: "more or less humanoid, but slender and frail, with gangly limbs and half-formed facial features. Its flesh is pale and hairless, and its eyes are vacant and white."
I think a more important question is why the wizard is trying to do something which is apparently very harmful to your characters. Presumably you're in a situation where having your disguise broken would be a very Bad Thing (TM), especially if the rings are left on.
These could even be nasty cursed items, given the nature of your party, so it's possible it may be difficult to remove them if the GM is going that route.
My advice:
See how the GM handles it. If he's going to let the party and campaign be destroyed by the errant actions of a single individual, perhaps you should look for a different game. It's telling that you would consider PVP as a solution in this group. PVP is generally a very bad idea for any campaign, unless all the players are mature and can conduct it in an agreeable and story-progressing fashion.
It's also possible the GM has anticipated these events, and this is the beginning of an epic quest to undo the magic of the cursed rings while evading the torches and pitchforks of the judgmental townsfolk.
