I've been in a similarity situation, but the women hadn't just left a marriage.
I would say, "You have 2 weeks to get a job and start contributing or you are gone."
Then in 2 weeks, when she 'calls your bluff'. I would walk her out the door and to the street, and say goodbye.
No Joke.
It's not cold-hearted... why should you support this drunken and lazy skag? She won't get her act together while she has a free roof over her head.
Hope That Helps