Do you think my neighbors will overreact if I ask them to keep their kids off my property even though their kids haven't tried to go onto my property yet?
I think it could be, how is your relationship with your neighbor?
They don't seem to like me and I think they'll react badly.
You have to be very careful what you say and how you say it. You could put up posted signs that establish the fact that no one is allowed to enter. I think you need to wait until you actually see the kids enter your property before you say something.
I don't want to wait until it happens to say something I want to do it now.
I think this could cause a further rift between you and your neighbor. You could put a fence around the property instead and then you wouldn't have to worry about the issue at all.