It seems as if she is trying to tell the new dogs who is the leader of the pack in your home. As soon as they enter, their appears to be an immediate power struggle.
You said you have other dogs that are permanent like your bulldog ... how many of these other dogs do you have and are they spayed/neutered. Also, your other permanent dogs .... how do they react to the newcomers. In other words, are they 100% submissive to the client's dogs. Also, do you run a dog sitting service? If so, how many new dogs do you get at a time?