How can you even consider losing peace between yourself and a neighbor over a few dollars? Especially when it wasn’t even their fault your kid hurt herself. I mean kids fall all the time playing. It could have happened at your house. So just because it happened at their house you should sue them for compensation and money? ha ha.
If you go to Court, it is always possible you would win, but what you would lose is much more. People/neighbors community would lose respect for you and maybe not be very compassionate towards you and your story. and how you will hurt that family is too much.
Big deal. You kid fell while playing at their house. Did they push her down? Someone hit her? So don’t send her there anymore.
But most likely she just hurt herself naturally playing.