This same neighbor told me this morning that he is having ChemLawn come and spray his grass to hopefully poison the food supply for the bluebirds! I don't know what to do.
Unbelievable of the insensitivity of this guy and what he is teaching his youngsters. Some thoughts of what to do: if you could get a video or audio of this ignorant behaviour such as saying he is having his lawn chem'ed to kill the food for the bluebirds - and post it - post it on youtube, post notices on the craigslist in your area. Also, write a letter to the editor of your local newspaper, perhaps provide pictures. What you may want is the public on your side and getting local media attention may help. If there is a local nature club, ask them to get involved. Also, if he is a practicing lawyer, perhaps some media attention will adversely affect his business or political aspirations, which is usually what such morons understand.
Also, check with the school his children are attending. See if a local nature club has been active there in educating the children the importance of wildlife and respecting it.
Also, borrowing a barking dog to bark at the kids playing on the slide may help in limiting their time on the slide. Or, doing something else that is "offensive" audioly (not sure if that is a word, but I think u know what I mean) to the younger crowds. Perhaps like playing some genre of music they don't care for.
Be careful on this one, your area may have laws concerning how long a dog is allowed to bark without being considered a disturbance and how loud a radio may be before being considered a nuisance.
I have two barking dogs that chase squirrels, and amazingly - and thankfully - my yard hosts nesting and feeding birds all year long. Including, a couple of years ago, a pileated.
Also, in response to the bluebirds: my father has had bluebirds nesting in his yard for years, and this year his neighbors put up a trampoline close to the bluebird house. I am not sure how often the kids play on that thing, but his bluebirds are doing okay and are now feeding the hatchlings. Hopefully, your bluebirds will be so resilient, too.