To me it sound like the male dog does not see your wife as his boss. The female may not either but definitely the male. They know you are the ultimate boss so they behave when you are home. I'm sure you have made it perfectly clear that fighting is not allowed when you are around. So they behave when you are around. When you are not around, the male feels he has to reprimand the female for any perceived misbehaving. Given the males size and weight, he is the likely alpha of the dogs.
Now your wife may be a contributing factor as well. If she has a preference for the female, the male may not like that the female gets attention when he isn't. As the alpha dog, he should get attention first, be fed first, come in and out first and even get treats first. If your wife takes turns or does it differently, the male will not be happy and take it out on the female.
To correct the behavior, the dogs have to see your wife as the boss behind you. The fastest way for them to learn this is for your wife to start obedience training with them as well. You might teach her your way or she can use the following site. Be sure and click on the link to the page on obedience at the bottom. and links on subsequent pages leading to detailed instructions.
Training works best if you train at least 30 minutes a day (two 15 minute sessions). I would start making your dog work via the Nothing in life is free program (NILF). It is outlined below.
Additional training can also help. Both dogs should be leashed and if one dog even looks at the other dog, a correction should be done. Any sign of aggression including a prolonged look, hair raised on the shoulders, a growl or even a stiff legged walk, should be corrected. A correction is a quick tug of the leash and a firm low toned "NO". Once she does this couple of times, she should notice the dogs ignoring each other. When that happens, she will want to reward them for the desired behavior. Again, use tasty treats like the hot dog slices. This teaches the dogs that she WILL not tolerate fighting in the pack.
It will help if she learns body language too. She will then be able to see what the dogs are saying to each other with their posture, tail set, ears, etc.
I would not allow them on the furniture. Dogs that are allowed on furniture (even if put on the furniture) tend to feel that since they are elevated to your level or higher if on your lap, they mentally feel elevated as well in the pack order and thus are the boss. Keeping them on the floor can help lower them mentally back to a submissive position in the pack. So the first thing is to not allow him higher that the humans or even on the same level. Attach a leash and use it to remove him from the furniture. Give a correction in the form of a short tug to get his attention and firm "NO" when he attempts to get on and a treat when he starts not trying to get on the furniture. Thus you are providing negative reinforcement for the getting on the furniture and positive reinforcement for the desired behavior (not attempting to get on the furniture).
If you want to pet them , then you can make them obey a command and then ask them to come up. Once done though they have to get down immediately on command. They should not be allowed to just get on the furniture at will.
I hope this information is helpful to you. If you would like any additional information or have more questions please don’t hesitate to press the reply to expert or continue conversation button so I can address any issues you still have . If you do find this helpful, please take this opportunity to rate my answer positively so I am compensated for my time.