TBH I have not really asked her if she's been dating as it's none of my business but then I would want to know what I am getting into before making any commitment.
She just wants a place to live with a flatmate she can get money out of. I guarantee you, she'll be going out and bringing guys home, then telling you she never promised that you'd be getting back together.
Either you'll leave and have to find a new place (in which case she's got herself a place to live), or she'll leave to move in with the next guy who she thinks is a better prospect.
The fact is that she wants to split with you and have her freedom, but the practicalities are that it's easier for her if she moves back in with you for a while. She doesn't care how it affects your life or feelings, it's just better for her. She's still looking towards that freedom and single life, and sooner or later she'll leave again.
Look at it this way. If this was a woman that you didn't know, and hadn't dated, would you be getting a flat together on the basis that you might or might not be in a relationship with her? It's ridiculous.
At best, you could both start again as single people dating, each living separately. to see if you can rebuild, but I think you know that all the trust has gone, and she can't be relied upon, and doesn't really care that much for you except as her security blanket.
Cut ties, move on. She's already done it, but doesn't have the guts to truly let go because she's scared of life on her own. Do yourself a favour and find someone else who actually wants to be with you. They you'll look upon all the things your ex said to you in a completely different light.