
It must be awful for you :( I really do sympathise with you as we had this problem many years ago. Luckily we were only privately renting, but the house next door was a housing association place and was home to 3 very unruly kids with a single mum that didn't have a clue on how to control them. (I am not casting aspersions on any single parents in HA places) :)
We had 2 GSDs at the time and the kids used to poke them with sticks through the back gate and throw fireworks into the garden

The dogs used to go mad at them! (they were lovely dogs who usually loved kids before this) We spoke to the mother many times and she just said "I can't watch them 27/7 and kids will be kids" in other words, she wasn't interested. We spoke to the Housing Association people and they sent them 3 written warnings, we also spoke to the police about them as we were scared that one day the dogs would bite. And although sympathetic to our situation, the police did say that if the dogs bit any one of them then we would be liable to prosecution and our lovely dogs risked being pts!!!

All we could do was keep the dogs away from the garden, which we did, for their own safety and our sanity and then the day we moved, because we couldn't stand it any longer,one of the other neighbours told us that there had been an eviction order served on this family. Its called sods law.
I know that you shouldn't have to keep your dog out of the garden and it makes me really angry that it always seems to be the innocent that suffer in disputes like this, but it really is the only option. Even if you could change the behaviour of the kids, your dog has already been "conditioned" against them. Sorry but I have been there and I really can't think of anything else that you could do.
Good Luck. :)