I suggest picking up the Nylabones. If Annie wants to chew on them, let her chew them *in her crate*. That way, you can close the door so that Pippin and Frodo can't bother her and she won't feel the need to lash out.

Annie does push her way around the house, blocking the other's way in and out of the doorway. She is very bullish with them. I don't know how to make it "even"...like who gets to go outside first?? who comes in first?? seems then I am encouraging Pippin to be top dog.
Rather than just opening the door and letting Annie gallop inside, teach her "Wait". When you open the door, say "Wait" and don't release her from her wait until she gives you eye contact. If Annie is truly dominant, the other dogs won't even come in before she does, so you needn't worry about who comes in first. To dogs, it's really not that big of a deal. Besides, if you teach "Wait", Annie realizes that YOU control the situation and that she should have no reason to aggress. FYI, my dobermutt, Ivy, is the bully. I always make her wait before she can come in. However, because Ivy is truly dominant over my greyhound, my greyhound will wait with Ivy, even though I never taught my greyhound the "wait" command. Alternatively, if you're really concerned about who comes in first, though, teach all the dogs "Wait".
- (If you need tips on how to teach "wait", just let me know)

Regarding the issue of beds, I would suggest leaving an open crate just for Annie. If she's attempting to push the others out of their beds, I would recall her and send her to her crate (not as punishment, just as redirection. You can also give her a treat in the crate so that she won't associate the crate with punishment). My dogs all have their designated spots. Nobody ever really intrudes. I do think they like the clarity of knowing exactly who sleeps where.

Again, practice that recall and do NILIF. Together, these two will build the foundation for a very strong relationship between you and Annie, and you'll become a very effective leader!