Just like the prior thread, this seems to breakdown to those who feel that no one should be allowed on their property unless asked and those who feel that yards are open to all as long as they are doing no harm.
I would guess this breakdown has a lot to do with the age of the posters and the way in which they grew up. I am older. I grew up in a small town in Iowa. No one thought anything about kids playing in each other's yards. It was such a small town. We roamed the town and played where ever we found a bunch of kids and had sufficient room for our games. One of our favorite games was to throw a ball over the roof of a house and then the person who caught it would attempt to tag the kids on the other side. If you were in the house, it was incredibly loud. None of the parents seemed to mind. We'd move from house to a different house each time we played so we wouldn't bother one set of parents over and over. Today, people would say that we were rude and disrespectful. That was not the case at all. The parents knew us and had no problem with how we played. If they did, we have a problem, we'd stop. We were actually very respectful of others.
Of course, back then, everyone in the area knew each other. If a family had a problem, the other families were there to help. If someone did break something, the other parents were always ready to take care of it. Now days, many people don't know their neighbors. They make no effort to get to know their neighbors. No wonder their is a sense of distrust and a fear that someone could cause harm. People today are so afraid of lawsuits. I find the whole thing rather sad.
Of course, it is the OP's right to decide who can be in her yard. Maybe, if she tried to get to know the kids, it would help. I've found most kids are pretty reasonable if you really take the time to talk to them.