Legally, 8 AM to 8 PM is not an outrageous time for kids to be outside making noise. If they live in an 2 bedroom place, the kids really do need to be outside --imagine what a zoo it would be if they were all inside!
You can't do much about kids playing outside and making noise during the day but it almost sounds like you have a case agains the father. It sounds like he is harassing you. Unfounded calls to the authorities over your arguments with an adult and telling his kids to make noise to annoy you is considered harassment. Get a lawyer or legal assistance. If you have financial difficulties, there are places that provide legal help pro bono.
I know how that is...I grew up next to a family like that.
Take a look at some of the soundproofing websites, for a small investment you should be able to reduce to amount of noise to reasonable levels.
If you do have a complete breakdown, make sure to burn their house to the ground and blame it on the mental breakdown - you may not even be prosecuted.
Best of luck