AITA: new neighbor keeps complaining about our dog in the backyard

So we’ve been living in this duplex for about seven years, the majority of the time sharing the yard with this really great neighbor. At that time, we had no issue with the yard being a shared space (we didn’t really have “sides”) and we were both dog owners, so we would have our dogs in the yard playing and they would do what dogs do and sometimes go to the bathroom there. Obviously we would always clean it right away and hose it down to prevent smells and keep it clean.

Sadly my awesome neighbor moved and the apartment next door is currently being inhabited by a single mom with two really young kids. They’re home all day and in the yard the majority of the time. When they moved in I welcomed her, let her know she can have access to everything in the yard including our furniture, gave her planters for her flowers, etc. I also have been trying to be super helpful, giving her kids free toys and art supplies (I had a bunch extra from work I was going to donate), offering to help her get furniture (she doesn’t have a car), and even helped her pay a vet bill because I felt bad for her kitten.

Anyways, lately she won’t stop complaining about the dog going outside. We’ve been extremely diligent about cleaning the yard, hosing it down, using soap after every pee and poo. We also walk our dog twice a day one hour at the park. She gets plenty of outdoor time but sometimes she does what dogs do and she goes in the yard. This neighbor will not compromise and I heard her bitching about it this morning, stating this is HER side of the yard and that we shouldn’t have a dog because we “don’t care.” She was bitching about her side of the yard as her two kids were lounging on my couches on my “side.” They have spilt their juice on my couches, left their toys everywhere, and the little boy is sitting on my couches with diapers and no pants.

Anyways: would I be the asshole if I just put up a fence and basically stopped talking to her? I feel like I tried so hard to have peace and a relationship with her but she’s making this so difficult. I feel sad but idk what to do. The reason dog goes pee on her side is because her side is literally just empty concrete and my gsd is intelligent and doesn’t go on carpet or anywhere near furniture. Again she won’t compromise despite us cleaning and disinfecting right away. I will also work with my pup to train her not to be on their side at all.