Thanks, everyone, for all the suggestions.
The music was cranked up yesterday by about 4 p.m. after the kids were home from school. The kids were out there screaming at each other. And by screaming, I mean actual screaming. It was constant screaming for an hour. That's when I left the house. Sometimes it's howling. They'll stand out there and howl at each other for hours. I had a work event last night. DH and I came home at almost 9 p.m., and the party was still in full swing next door. Music blasting, large group of people, the kids were still shrieking, dogs barking, etc., etc. They were out there well past 10 p.m. And (supposedly) there's school tomorrow. At least for DS there's school tomorrow.
DH and I have talked about our options. He said "take them to court" last night, so we're going to begin the process of gathering data to support a case. Really, we think it's either that or move. DH also is going to do some additional research on the noise ordinance, particularly weekday vs. weekend.
Where the kids and their toys are concerned, when they come to our door, I think we'll take JenJay's suggestion. We will tell them to come back later and look on the porch for their item. If it isn't there when they come back, that means we haven't had time to look for it yet, so don't ring the bell or knock again. Their items will be mixed into a bag with their trash. If it happens again, the toy(s) will go straight in the trash with their trash. If the parents don't like it, they'll have to talk to us about it.
I've never heard of a noise repellent machine until today, but I looked it up, and I'm intrigued.