Dog Fights

I'm having dog issues. Dupree, my female pug has hated my female bulldog Coli since they met. 99.9% of the time they tolerate each other, but on occasion, usually when I'm alone with them both, she decides that Coli has committed some serious crime and should be punished.

I pull them off each other and separate them instantly they aren't seriously hurting each other, but it has to stop. I usually see the warning signs and try to prevent the fights, but it almost seems to escalate things. I think the problem is that they have been in a battle for dominance since they met, and it never gets sorted out. 

I have a strong suspicion that I'm the cause of all of this. Dupree is very bonded with me. I think I've been marked as her property. Coli is hesitant to come when I call. I think she's afraid of getting in trouble from Dupree. Both of them usually listen to my commands, but when they are about to fight, it is like I'm not there. They both ignore me. I've tried to "Cesar" them. For small misbehavior it works, but not for the fights. I don't really walk them. They are both older and have the typical smooshed-face dog illnesses. They don't seem to have excess energy. I have tried walking them together in the past to promote bonding, but it never made a difference.

I totally love my dogs but I'm starting to consider finding a new home for one of them. I've had Coli since she was a puppy, for 11 years now. I can't imagine not seeing her every day. Dupree is a pain, nobody who knew her would want to deal with her, and I love her to pieces. Anyone with any experience in multiple dog households please share!