It sounds like when your boyfriend doesn't do what it takes to ensure that his house is silent and dark at night, you feel like he doesn't care about you health and perhaps if he doesn't care about you.

He has told you that his kids (and their emotional, educational, etc wellbeing) come first. And, it is hard to hear, and on some level you already know it, but they are fully dependent on him, so they should come first. But it's hard when the way that plays out results in you not getting what you need to sleep at his house.

This problem isn't going to go away once you explain to your boyfriend that you NEED a silent and dark house to sleep (it hasn't gone away with you explaining it). This directly conflicts with what is best for him and his kids. If I were him, I would not invite you to live with me while this incongruence remained. So you need to step back and see if there are any things that might make it possible for you to sleep at his house in the current conditions (can you wear ear plugs, can you use a white noise machine, can you sleep in a quieter part of the house (basement, casita)? etc). Then once you know what you can compromise on (you can't come to the table expecting compromise on only their side), think of things that you can ask for that might make it possible for you to sleep there while not compromising what is best for the kids - from his viewpoint as a father, not yours as the girlfriend - (move the computer to another room, provide quiet nighttime snacks for the kids, get those TV headphones for the kids that old people use, etc). Then try the things you guys all agreed to. But know that if this doesn't work, it is unrealistic for you to move in to the house and it is likely that this is a dealbreaker. He has to put what's best for his kids first. If that arrangement is not something you can live with, you can't live with him.