Ooooooooh, I can see it from both sides. Unfortunately when people have kids, and I include myself with this, they become the centre of their world to the exclusion of everything else around them.
My last house had little soundproofing, next door had a screaming baby whose room was the other side of my bedroom wall. I felt as though the darn thing was in the room with me! Not forgetting I could hear the parents having sex, talking, walking up the stairs, opening and closing doors.
It’s downright miserable!
Seriously, you need to calmly speak to them about it. The onus is on THEM to deal with it, even if that means moving child to a different bedroom. You shouldn’t have to put up with it.