That crate must be huge.
Please let her have her own crate.
I allow my 4 to each own, their own crate and what ever is in their crate. I believe that all creatures need a tiny space of their own. My dogs don't have high and mighty attitudes in extreme but, are Yorkie proud, they know I am the alpha. About fighting just watch and let the dogs know that is unacceptable, they will decide their own place in the pack. As the leader you do not have to allow them to fight.