No, the mother can't just come and go as she pleases and she can't just kick him out. He's got a contract (a written one I hope) and, as long as he's paying on time, she'll be in breach if she tries it.

By the way, Joe's girlfriend was Joe's TENANT and, as such, he could have kicked her out at any time with proper notice, typically a month, but since she has abandoned her tenancy he's free to change the locks and not let her or the mother back into the house.

I strongly suggest that Joe consult a real estate attorney and have his contract and his situation reviewed so he can learn how to stand up to the mother. A letter from the attorney to the mother is likely to put her in her place and get her off his back.

The sooner Joe resigns himself to getting a lawyer's help, the less he'll have to worry about.

PS: No need to post the same question twice. I deleted the other one as a duplicate. Please keep all your discussion on this topic to this thread.