I'm also not an attorney and am not giving legal advice.
If he's not on the lease, in my opinion, he has no right to be there and can be selectively evicted if you like. However, from a practical standpoint, I wouldn't do that unless she is agreeable with that plan. If he's not on the lease, and she wants him to stay, I would qualify him and include him, if he qualifies, on a new lease with them both. At that point, they can be jointly considered as "the tenant" and can be dealt with together as "the tenant" and evicted if they violate the lease.
As far as trying to resolve issues between them, or for that matter between different tenants in different units in a multi-family dwelling, I would refer whoever calls you to the police unless one of them reports a VERIFIABLE lease violation. It's unwise to try to take action as a landlord on a "he said / she said" type of domestic story. I get that stuff from time to time, and I almost always refer people to the police. Usually they tell me they already have called the police and that the police didn't do anything. When I hear that, in my opinion, it's a really good clue for me to stay out of it as well.
For more of a "warm fuzzy" on this, I recommend you consult with a professional property manager, or, as others have said, hire an attorney.
Thanks,
Robin