If you are living paycheck to paycheck, you need to reevaluate your living situation before committing to renewing the lease in your name. It is a plus that you are employed, but the financial problems of single parents are well documented. You have no backup. In addition, besides your shared young children, there was an older child present for your Christmas week mess. Your shared children are at the back of a long line for your DH's resources.
And, the additional information you provided makes you look really bad. He had a history which you chose to ignore when you became involved with him. I suspect that the "bad boy" was attractive to you, and you participated in that lifestyle before you had the responsibility for 2 children.
I hope your therapist is helping you understand why you have made questionable choices and is not just making suggestions on what you should do now otherwise I would expect you to go from one toxic relationship to another.