OK. There's a lot I'm not going to say, and some things I am.
Dogs do realize a changing of the guard. My oldest (I live with three) lets my youngest get away with stuff she never did with my middle dog and my deceased dog. She knows it's easier for her to just let him have his way, but she does still let out a snarl once in a while. And I let it happen. Reason being, dogs left to their own devices will pretty much sort things out on their own. While you should always be boss, they still need to feel like one of them has a higher ranking in "the pack". And if they are fighting in front of you.. I mean, all out fighting.... you are not boss or have not let them decide who is top dog amongst them. Because once they decide who the Omega is, there should only be a snarl to remind the other one. They would never get "into it" in front of the Alpha, you. That's a little bit about being a pack.
The other thing to consider is that Inu breeds have a tendency to have attitude changes when there is a thyroid problem. And for some reason, vets do thyroid checks as a last resort to determine a skin or attitude problem. And 9 times out of 10 the dog has a thyroid condition that a pill clears right up. (BTW, the neutering and spaying will have zero effect on an adult dog's behavior once they have developed. And your two have even mated, which does compound things.)
So I guess I would ask myself a couple things;
Are you the boss? If they are fighting in front of you, you've got a bigger problem.
Do you let your dogs bicker amongst themselves or always intervene? If they can never figure out who is top dog by themselves, each fight will get worse.
Have you had a full blood panel done on them recently? Or at least the female? The thyroid problem is probably not too high on my list though, but it still happens frequently with that breed type. And you did say several times how hyper she is.
Just some random thought...