and her roommate had to leave because of her.

You could also rent out as a whole unit but include a slight increase to rent if that unit is going to have a pair of roommates living together.

If a tenant wants a partner or roommate to move in, I do a background check.

(We see a lot of clients do this like these two, and if I were in your situation this is what I'd do, but that's only because I'm only so fond of other humans and don't want roommates.)

For example my first house hack I bought a SF home and my PITI was $2043, I got 3 roommates whose total rent was $2300 per month, utilities included in the rent.

I had an old roommate get his trash pile of a car towed away.

I have two roommates as well. 

My daughter attends University of Indianapolis and rather than paying her rent to live in someone else's apartment, we purchased the home to save the rent and also to have a roommate live with her and cover the mortgage and insurance.

Single-family home with roommates?

If she wouldn't have income qualified on her own, I think you may need to have a long talk about her getting new roommates, and that the jailbirds are NOT allowed to return -- not even "just for a few days".