You're in a good position at the start of this process (versus looking back after a whirlwind of changes) to decide how you want things to go, based on what's best for the kids. As I'm sure other members will mention, when it comes to custody/PT, setups that were supposed to be "temporary" or "just until he/I get on his/my feet" tend to become permanent.
I'd recommend discussing with your L any implications (for custody/PT especially) of moving to the apartment that you might not have thought of or that might not be clear or obvious at the moment.
Yes, I'll mention it, well, at least mention what I'm thinking. Ponder with your lawyer what impact any of these changes will have on your being the Primary Parent. Whatever you call it, custodial parent whether joint or otherwise, majority time parent, decision maker, tie breaker, etc. If you are the more stable parent, as you demonstrably are, then you need to do everything to reflect that you're the stable and more capable parent.
Is it his home or is it instead jointly owned where you have a financial interest in it as marital equity? If your state's laws default you to the driver's seat in certain aspects of a parenting case, then don't sell yourself short. Especially don't Gift Away any advantages you now have, you may have a hard time getting them back. All I'm saying is that us Nice Guys and Nice Gals here have personalities that often impel us to be overly fair or overly nice when doing so could sabotage us in some legal way. So before you make major decisions vet them with your lawyer, perhaps here too in peer support. You moving out versus him moving out could be one of tat type of decisions. However, doing one or the other is not necessarily bad, many parents have found establishing a fresh new (and stable) home to be empowering. Just do it for the right reasons and the right goals.
I have now accepted I have to be the one to make the changes I need.
That is a major theme emphasized here. We can't fix a seriously disordered spouse or loved one. Yes, we can support him/her if seriously pursuing therapy and in the process of making lasting improvements, but the person needs to do the hard work, that part is not up to us. So often it comes down to boundaries... .our boundaries. We can't make the other do the right things but boundaries are how we respond to poor behaviors... ."If you do/don't ___ then I will/won't ___."