I totally agree with Sabby and Gimmeice. As i read your post, I recognized some of my own behaviours in what you are trying to do...work with everyone, be a conscientious employee (which SHOULD be appreciated by your employer, by the way).
I agree that you should just go ahead and state the time you're taking off, and let the others work it out for themselves. They obviously don't appreciate your efforts, and even seem to be intentionally making it difficult.
Patty