I have great sympathy for you as I also suffer from noisy neighbours.
I don't think it is rude or inappropriate to go round (at a time when they are not being noisy and you are not at the end of your tether) and speak to the family.
You can ask whether they could try to keep the noise down after (say) 10 p.m. If you phrase it as "I'm sure you weren't aware how much noise can be heard in our house" so you are letting them know that you assume they don't know that you can hear.
It may be that they genuinely don't realise that you can hear them (I had a neighbour who was very mortified when she realised that her teenaged daughter's constant loud music was disturbing me - it was much louder in my living room than it was in my neighbour's own living room - as soon as she knew, she made sure that the noise was kept down, it had simply never occurred to her that it could be heard in my house!
If the neighbour is not receptive to a polite request, don't take it further with them.
I would also second the suggestion of white noise - I have found that using a white noise generator (I found a free app for my phone which generates white, pink or brown noise) does reduce the disturbance from my noisy neighbours, and in this recent very hot weather I have several nights ended up sleeping with the window closed and a fan on, as several of the neighbours sit out very late on the pavements and it is too noisy for me to sleep with the window open. (I do feel that they are very inconsiderate, but in my particular case I know that there is no way they will change their ways, and this at least means I can get some sleep!)