I would absolutely talk to her mother, if it were me. I might not go into that much detail unless her mom asks you to explain, but I’d just say that things are not working out but there is an issue with her having someplace to go once she moves out of your house, and then simply ask if it would be okay for her and her kids to move back home with her until they find a place. If her mother says that she can move back, then that means you will know for sure that she has a place to go and she can’t tell you otherwise. Then it becomes she doesn’t WANT to go rather than she CAN’T go, and, honestly, that’s not your problem. As long as she lives with you and wants to be with you, she will have absolutely no motivation to actually leave or find a place… but if she lives with her mom and doesn’t want to live there, it’ll give her the motivation to find a place, which will be much more helpful to her in the long run (she’ll be growing and moving forward rather than staying in a relationship with someone who isn’t happy). Know what I mean?

I agree that it would be great for you to just be alone for a while and get back to being yourself and doing the things you like to do. I’m sure your daughters would love that, too. If you fall very quickly when you date, though, I would hold off on that for a bit. Just hang with friends and do some new fun things with them instead.