Before I saw your update OP I was going to say they're not likely to give a shit.
I had same problem. All our rooms (and the objects within it) rattling all day long with kid doing cartwheels off the ceiling (what it sounded like), gone midnight and early in the morning. They never actually thought to ever take their kids out to either of the two parks that are a 5 min walk away, ever. Or, use their back garden for 'running around'. I wore headphones 24/7 (except sleeping because my ears got really sore) and it did fuck all. You could not only hear the noise, but fucking feel it. Then we had to deal with the parents getting pissed and having overly loud shagging sessions at 4am - they slept in the day when kids were running amok (I know because you can hear when the adults are up and about). I basically got very ill with the stress and was genuinely on the verge of a breakdown. I spoke to them 3 times, and my partner did, and then took to texting them when it really got too much.
And they had carpet down. So you have no idea how sorry I feel for you right now. Btw - I thought there was a rule about not having carpet down in flats where you are above people?
Not everyone can afford to live in lovely 'detached' houses in the middle of nowhere like is the common mumsnet response when people complain about noise from other folk. We're hardworking people and we just couldn't afford to move.
We did speak to their landlords and they didn't give a shit either. Was quite glad when said awful neighbours suddenly skipped rent and did a runner on them, and it turns out the landlord had to do the place up because of the utter shit tip they'd made.
I hate to say it but you're likely not to get anywhere. A lot of people (note that I am not saying ALL), with kids are used to the noise, unaware the effects it has on other people, and when it comes to having to control their children or altering how they live to accomodate/consider others, their attitudes quickly turn about as selfish as they come. There's a reason noise has been used as a form of torture. If you can, move. If they refuse to be considerate, I hate to say it but refuse to be considerate back, that's the only way people like this get the picture.