I don't have an opinion about joining your particular union, but I would only do it if you think it's worth the money. I agree with Winged...doubtful that the union is going to go to bat for you if you get into a knock down drag out with this attending, but I could be wrong. You might want to talk w/one of the resident union reps, in a quiet fashion, only if you feel the person can keep his/her mouth shut and not gossip about this.
I do think you'll get further by just sucking it up and being the very best resident you can...IMHO that tends to be the best defense in these type situations. I have had attendings who I think didn't like me much, but the thing is there were a lot of others who DID, and I think/hope most of the other residents as well,so the ones who disliked me I don't think would have gotten very far had they tried to hang me out to dry. That's what you have to do...try and make yourself bullet proof. Work harder than anyone else and be nice to everyone, and try to be as smart as you can (i.e. study). Also, don't let this one person drag you down mentally, if possible. If you do feel that damaging things are being documented, I'm not sure how you can defend against that, other than writing really good notes/documentation and trying to take extra good care of patients on that particular service w/that attending. It is no doubt a difficult situation, but I'm not sure the union can bail you out of this.