How should I handle hostile neighbors?

I moved into an apartment this week. I have an 8 year old son. My brother came to help me get settled and brought his two sons who are 6 and 10 years old. To get the kids out of the way, it was suggested that get their Nerf football and go outside to play. They were out about 10 minutes and I heard someone yelling. I went out to see what was happening and the women next door was screaming at the kids that they were making too much noise and were on her property. She said if they came into her yard again she was going to take the ball and keep it. I told her that the kids could play anywhere and for as long and as loud as they wanted and if she confiscated the toy, I'd call the police. Then she said anything that came onto her property was her right to take, but she didn't expect "trailer park trash" to understand about property rights. Why is she so judgmental? If the noise of kids playing bothers her, she should just get a place in a senior community. Who is right in this situation?

It sounds like she is being completely unreasonable. I would just make sure that your kids are doing the best they can to keep the ball in your yard and not go onto her property. If she does take the ball, call the police. She has no right to keep it, but your kids can't go onto her property. Just take normal precautions. Don't tell the kids to be louder just to bother her (re: the they'll be as loud as they wanted). That will just make the situation worse. You are right, technically speaking, but a lot of old people just forgot what it was like to be young and have fun.

You are.
She can't take the ball even if it lands in her yard, that would be stealing.
Kids at play do not make that much noise, the police wouldn't do a thing about it.
I'd stay away from her, she sounds like she's bitter.