Check and see if your state adheres to the Warrant of Habitability. The Warrant of Habitability states that your landlord is required by law to provide a safe, clean and habitable residence. Not all Warrants are the same however.
We had terribly inconsiderate, rude, and ignorant neighbors living about us while I was pregnant with my son. They too never took their daughter out to the park to run around. The mom also claimed that she had to put her daughter to bed between 11pm and midnight so that she would sleep later. Ohhhhh those horrible nights listening to that young child jump off the couch, dump blocks on the floor, walk around with bricks tied to her feet. LOL
I too was very nice when I would go upstairs to speak to them about the nightly noise. I NEVER complained about any noise that was being made during day. I did keep stressing how they were going against their lease by allowing their child to make as much noise as she was after 8:30pm. This of course fell on deaf ears and they did begin making more noise just to spite us.
****To the poster that said that you would have done the same. I just have to say that is the most disrespectful, inconsiderate, immature, and childish way to behave. I would also guess that you don't have small children running around above you all day and night. It's usually those that don't that don't think this is a big deal.
Anyway, I began documenting the dates/times/noises that were being made. I did this on a daily basis and then compiled all of them and went to my leasing company and explained the problem. They contacted these neighbors, explained the situation and told them they needed to carpet 80% of their floors. These ridiculous people then began banging on my door when they walked by, yell curses outside my door, and had the nerve to send the wife's sisters downstairs to talk to me. Well, they were also unreasonable and tried to bully me. When one began yelling at me I called 911.
I must add: We were not in any way creating any noise or disturbance to this family. We only asked that they respect the fact that we were living below them. They couldn't.
I returned to the leasing company, handed them the 20 or so pages of noise documentation I had and told them that my Warrant of Habitability was being broken and either they take this matter seriously or we would either have to go into mediation or skip that and go directly to our lawyer, who said that we had grounds to make a case against the leasing company for not dealing properly with tenants who were breaking the common lease we all have.
They sent a letter to these tenants quite quickly explaining that if the didn't stop they would begin the eviction process. I was shocked! It worked!!! Well, within weeks those tenants moved out and we have never heard or seen them again. Aaaahhhhhh.
Good luck to you. I absolutely 100% understand how stressful that noise is and how thoughtless so many people can be.
Peace.