When you say they are not going to stop until they kill each other, you need to clarify if you've ever seen two dogs go at it until they killed each other. If two dogs are not going to stop fighting until they kill each other . . then you must be talking about two game bulldogs here? Because 99.9% of all other dogs WILL STOP before they kill each other. I can promise you, that if two dogs are trying to actually kill each other, then aint no water hose, or tree limb or shock collar is going to stop them. What most folks don't understand is what stops dogs from fighting is heat and exhaustion. Ive seen guys spray dogs with water hose and all it does is just cool them off so they can fight longer. A shock collar will just make them bite harder, especially the one getting shocked. He will confuse the "shock" pain as coming from the other dog biting him, and then he just bites and fights harder to get the other dog off of him. As for a tree limb, well, if your talking about two gamedogs, then all you're gonna do is just get tired from beating them, cause they aint stopping.
Now if your talking about just two old hunting dogs, then I promise you, they WILL QUIT.
If I had a hunting dog (hound, cur, etc) that fought other dogs like you are talking about, then I would just get rid of the dog, lol.
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Question is how much do you like or need both of them? If you dont need both then like someone said just find it a new home, if you need both then you have basically two choices, one is keep them separate, the other can take a lot of work depending on their level of dog aggression and how much they see you as the master. Meaning do they respect you more than they hate eachother? They need to know that it is not tolerated and what they will get from you is worse than the hate they have for eachother. Just some food for thought and my opinion. I wish you the best of luck with them, I'm sure you will get it figured out.