A lot of this will depend on how the new dog reacts to your female's attempts to be the boss. Take the female with you when you go to pick up the new dog and stop on the way home to introduce them on neutral ground. I generally do not interfere in dominance battles unless they start to incur vet bills, which will happen when you have two animals which consider themselves to be equals in the Alpha department, and in that case the dogs are separated for life.
Other problems occur with dogs which, for whatever reason, lack social dog skills, and invite dominance displays because of their rude behavior. I see this a lot in young labs; I had a client whose rude pup wound up with a stitch job to the head; he was more respectful for a couple of months and then started soliciting a thrashing again, so I set him up with one of my bitches to remind him of his manners. She gave him a real CTJ, totally bloodless but very effective, problem solved.
The lab and golden think: "My humans give me food, shelter and love; they must be gods."
The Chesapeake thinks: "My humans give me food, shelter and love; I must be a God."