The real issue isn't his housemate, it is the life stages you are both at, they do not match. I hate to say it but this is a real killer in a relationship. There is nothing you can do to match up your life stages, there will always be a disjoint. It causes real resentment, it will break up your partnership eventually.
You say you have had a serious relationship for 2 years, but you haven't, you broke up and only got back together months later, you split over something that, had you both been at matching life stages, would have easily been sorted out without a split. This is not a serious relationship. Knowing someone as a friend is a world away from knowing them as a life partner.
Your DP is off on nights out and weekends away without you, if he was ready to make you his life partner he would be taking you on nights out and you and DC on weekends away and only occasionally going on nights out and weekends with friends on his own. He is still living the single life and enjoying himself.
When the reality of living with a DC in the house and the freedom it will curtail hits he is in for a shock. You both may try and make it work for a while but you will both come to dislike your situation. You and your DC need more than a DP who isn't ready for this why put the 3 of you through it?
Right now he is on his best behaviour and so are you, the relationship is shaky, you've already broke up and not been together for months, then back together again, that's fine when you are carefree and single. Your DC doesn't need this level of turmoil in their life.
You have been through so much in the past few years, I really feel for you For your own sake and that of your DCs, you need some therapy. Your DP has not and won't be able to understand what you need as he has yet to go through it in his life, he is at a different stage.
Moving in with him for no good reason i.e. because you don't like him living and prioritising his housemate is not a good idea. He is not committing in the way you want or need, that's not because of his housemate, it is because of him. That is who he is right now, he won't catch up on your life stage, he needs to go through stuff himself to get there by which time you will have moved on further too.
You will be better off finding someone who is more on your wavelength and ready to settle, whatever your DP is telling you right now is because he doesn't know what he will be getting into, he is likely to want to jump straight back out again when reality hits. This won't do you or your DC any good.
Let him go, work on healing yourself because you have had a tough time and find a DP who is ready to settle down properly.