I have some problems with the dynamics of my cats, too. They all get along with the dog, but each other is a completely different story.
What we did was provide each with their own area to claim, and some are traded often. Basically, by having enough perches off the ground they're allowed personal time without feeling the need to escape. Cat walks and perches help tremendously when dealing with bickering or fighting cats. The more space they have to roam and oversee, the better. It provides them a sense of confidence and security over the home, whereas cats on the floor can get a little snippy.
The addition of treats (especially if clicker trained - I'd click one and whistle for the other so as not to mix signals) decreases the stress/fear even more because it adds a positive note to the animal they hate.
But most importantly, you/she/whomever will want to start things off on a good foot by slowly integrating new cats versus letting a new one wander at their own risk. This can be done long after adoption even. Give the aggressor a few days alone in their own room, then begin the slow reintroductions with a lot of treats and praise for good behavior.
As for the dog, as long as he's not actively seeking them out, he shouldn't have many obstacles with gaining their trust aside from time.