I agree going and talking with the neighbors is the best ( and only ) think you can do. Unfortunately, I think you also need to prepare yourself for the possibility that the kids will continue to be loud, and do what you can do minimize the noise that gets to your child's room. A fan, a white-noise generator, etc. are all good ideas.
In our case it's not kids, it's our neighbor's large tropical bird that screeches loudly. We've good relationships with them, we've told them that the bird bothers us and they are aware it's a problem, however they insist there's not much they can do short of giving the bird away. We've just had to manage on our end how we deal with the noise. Unfortunately overlapping noises from ones neighbors are one of those things that there just aren't a lot of good solutions for.