I’ve never had a kid that big yet, so I can’t really speak to your exact circumstances, but I do have a nearly-teen autistic daughter that used to be very difficult.
I’d say reward progress and reward good behavior. Do stuff to move him forward, rather than making him comfortable where he is and make sure that whatever you are doing on your side is something that you can stop doing as soon as he stops holding up his end of the deal. The awful danger in moving into your house (even if he was lawfully married) is that he won’t be motivated to find work and life will be so comfortable that he and his family won’t ever leave of their own accord.
I’ll give you an example of a deal I have with my mildly autistic 12-year-old. She currently has an inexpensive ukulele that she bought herself and she’d like a nicer, bigger ukulele. I have the following deal with her. If she does 50 practices of 15 minutes a day, I will buy her a ukulele of no more than $100 in value. If she wants a ukulele of $200 in value, she needs to accrue 100 15-minute practices. If she wants a $300 ukulele, she needs to accrue 150 15-minute practices. It’s all on her how fancy a ukulele we are going to get her. So far she has done 37 practices and she’s going strong.
That’s the kid version of what you may wish to do, but think about how you would do something like that for your son. Perhaps, for instance, if he moves to your area, you could pay him for yardwork and odd jobs (on generous terms and maybe letting him use your stuff, but paying AFTER he does the work).
(I mentioned earlier the idea of paying son and his girlfriend $100 per personal finance class attended–I don’t know if that is within your means, but I strongly suspect that having son and girlfriend and two kids move into your home would be much, much more expensive than that.)
Dave Ramsey’s The Legacy Journey book may be helpful to you. One of the examples he gives in the book is that he had a matching program for his teens and their car savings. If they saved $3k toward a car, he would match it with $3k, so the teen would have $6k available for a car, if they saved $5k he would match it for a total of $10k, etc. By the time his third kid reached car-buying age, the third kid had BIG ideas and even bigger savings. I think it could be very helpful if you were to figure out some sort of arrangement like that for multiplying your son’s efforts for him, but in order to do that, you’d have to have open lines of communication with him, and to know a lot about his life, his aspirations, and his needs.
Best wishes!