I am assuming the dogs tolerate each other until put in situations that cause fight like the "DUH" stuff: feeding them together, letting them rough house, letting them have high value toys/treats together, leaving them alone together, etc.
Well, i've notice a few cuts and such on Buddy due to their rough play.
Then they're not playing. There can be accidents here and there, but dogs have exceptional control over their mouths.
As for the rough play: NO MORE. This has gone waaay past a "let them work it out" situation. No more excuses. They're not "just playing" here. The owner needs to step in and sort it all out for them. If she wants them to play and is willing to take the risk and precautions, fine. I would NOT recommend letting them play with "full tanks" of energy. My dogs cannot. They get exercise (treadmill, fetch, tug and--hopefully soon--biking) and then they're allowed some light play in the house. Emphasis on light. For my house, letting my dogs get all their energy out with each other is asking for it. High arousal levels can easily turn to fights. This is another point I should call out...The owner mentioned that Baxter was/is extremely territorial. If he is that way, then both dogs should not be outside together off leash. Someone walking by or something making a loud noise could set Baxter off and he could easily redirect on the other dog. The owner either needs to get the territorial-ness under control, or not have the dogs outside together off leash.
The owner also needs to get amazing, turn-on-a-dime recalls with these dogs if she wants them to continue playing. The minute the play begins to escalate, she needs to recall them and put them in a down-stay for a few minutes so the dogs can get their brains about them. Then they can resume playing. If they ignore her, then the owner has a problem. Both dogs need to be grabbed (good idea: to keep long lines on them) and put in serious time
out with a cue word ("TIMEOUT!!!"). Every time. The owner must now keep an eagle eye on her dogs and watch all of their interactions. She cannot let them just have it out. The owner needs to go back to strict NILIF, too.
If the dogs go for each other right off the bat, then I would place my money on crate and rotate. If they're just fighting constantly, same answer. If she feels she cannot handle the new responsibilities, same answer. I would strongly recommened the dogs take time away from each other (C&R) while the owner creates a game plan to deal with this situation.
That said, it would probably be best to contact a behaviorist to come and evaluate the situation hands-on. I would not want to rehome this dog myself, as he has shown aggression to people.
I do feel bad for this owner. She sounds very overwhelmed with the whole situation, understandably. I wish the owner luck. Inter-dog aggression can be difficult to deal with and is very stressful.