Welcome to SR, CourtJester. I'm sorry you are going through this. I wish I could say it was rare for this to happen, but, unfortunately, it's not. Addicts who go to rehab or NA/AA oftentimes are at a vulnerable point and it's not unusual for them to feel a kind of closeness or identity with someone going through the same things.
In spite of all that, that is no reason for him to treat you the way he is and has been treating you. You deserve better than that. I would suggest that you speak with legal counsel to find out exactly what your rights are. After 18 years of marriage, he can't just walk out without providing for his children.
If you are a named account holder in a joint bank account, that is good. You have every right to half of whatever is in that account. After talking with counsel, I'd open an account in my name only, at a different bank, and move half the assets from that/those accounts into it. If he has already decided to leave you, then you must protect yourself and your children.
I'm glad you found us. You'll find a lot of support here. (((HUGS)))