He's not well, is he.
Whatever it may be, depression, ADHD etc, he needs help.
And it seems both his parents have failed him. Failed to teach him and support him and see when things were going wrong and get him that help when he was younger. Poor lad. Life must seem a bit bleak, and I don't see much sympathy coming from you either.
But the thing is, this is your home, your own younger kids. You will probably be the one doing all the stuff around an extra person living there, not your husband.
It's absolutely normal that you don't feel the same way about this young man as he does. And that your concerns for your own sons wellbeing are setting alarm bells going.
If it was your own son you'd probably want him near you, and I'd imagine your husband is very worried - but being rubbish about expressing it. The threats may be his fear lashing out. Remember this is the man who brought this son up, his own mum's washed her hands of him, so it all sounds quite dysfunctional.
Might there be a compromise?
Boundaries and rules - your home, you get to set them too.
It would be a condition of moving in that first he understands the rules.
Doctor's appointments, therapy as needed must be attended. Any problem with that, it's his father's duty to support and facilitate that, not yours. A condition of you agreeing.
The room must be kept clean and tidy and hygienic. If he doesn't do it, his father will do it. And the laundry. Not you.
Your husband will take the responsibility for him, not you, and if that means changing his plans, missing work, tough.
If his sons behaviour towards you or your own children is cause for concern, he leaves.
And your husband will stop issuing threats.
This could be the best thing for him, and for his father. And you'll have been part of that.