I think your pup might be asserting her dominance in the "pack" through this behaviour. I let my two sleep on the bed with me but they are invited onto the bed once I'm settled in. If they are on the bed before I get in they are told to get off until I'm ready for them to join me. Just doing simple things like that might be a part of a solution.
As to attacking the other dog I'm not sure about that. I've always let my two sort out any dominance issues themselves. I figure they can talk "dog" better than I can. But that's not much help to you if you think some actual harm will come to one of your dogs.
I would not tolerate any dog fighting on my bed - especially if I was in it. When my two start any dominating behaviour on each other they are told to get off immediately. After a "cool down" period I invite them both up again. Even if you aren't in the bed that is still you designated sleeping spot as the "alpha dog".
But also bear in mind some of us are just grumpier when we are woken up - I know I am!
I find that training builds a healthy, loving, respectful relationship between you and your dog. I hope some of this is helpful to you. When it comes to training you've just gotta do what works for you and your dog.