Btw - what has he told you about OWs status? Did she break up with him? Did she move away to get away from him, or was she expecting him to move with her? Did he cheat on her too? I’d sure want to gauge how likely he is to swing back to her before letting him in my home.
Plus - do you want to put your son through re-attaching and then separating again? Or are you considering this move as a way to ensure that your son is safe with H? So you don’t have to worry about him being alone with H? If so, what’s your endpoint? What will you do if H refusss go move out again in the future?
What is your financial plan for the future? Have you discussed with an attorney what you might get in support if you divorced?
Also - Will having H there make it awkward for friends and family to come help? Do you really want to be responsible for managing his depression while dealing with a newborn? I’m worried he will be more trouble than he’s worth, which is why I argue for him keeping his own place for the first month until you see how this goes.