My neighbor and I are fighting about our dogs. What do I do>

So my neighbor and I are having an argument about our dogs. This originally started before either of us had a fence and one of my dogs got out to play with hers. Her dog attacked my dog and my lab then charged and attacked him. Long story short, all three dogs came away with scrapes, as did her mother. We offered to pay for all medical bills related to this incident, of which there were none, and agreed to put fences up in our yards. The fences went up and our dogs still don't like each other. About a year ago, her dog and my lab charged each other through the fence. Her dog was able to bite my dog under the eye, we took him to the vet and the puncture was glued shut and we were given antiseptic. She said that the blood in her dog's mouth was from a cut he got from my dog, even though she couldn't find it.

We decided to temporarily text each other when our dogs go out and continue to work at training our dogs to ignore the fence. We have done so, and our dogs only go at our shared fence when her dog charges. My wife and I decided we no longer wish to continue to communicate with them every time we let our dogs out. This is a problem because our neighbor refuses to attempt to train her dog to stop charging our fence. She keeps putting the blame on us and says she "isn't a dog trainer". I told her all this today and she said she is going to keep texting us. She also said that if our dogs attack hers, then we will be responsible for the vet bills, which I agreed was only fair if the reverse was also true. She said no. She then said if one of my dogs happened to kill her dog, I would have to get rid of it. I told her I would follow the law not whatever she decided. I am livid at the moment because she refuses to accept any responsibility. How should I procede in this situation? I want my dogs to enjoy their yard and I want my neighbor to leave me alone.