When he gives her treats, make sure he makes her 'work' for them. So have her "sit" and "stay" then he can give her a treat. That will help her understand he's in charge, and must be obeyed. Dogs love structure, so not necessarily gating, but giving her an area that is just hers like a create, so she has a "safe haven" and a place to retreat. For my brother's dog, it was under the kitchen table, another dog I knew had a playpen that was his "crate" and became his place to retreat to. Even when the actual playpen was eventually removed, he'd go back to that spot for his naps.