I agree with what the others before me have said. You seem to be rather intent on being right and making your daughter out to be a liar so you can prove your XW is the bad guy. As I know I have said before, as have others, you CANNOT control what your wife does or says, so focus on what you are doing and saying and how you can interact with your daughter. You've lamented not being able to see her over and over and when you finally did get to see her, albeit in a therapy session, you spent that time saying "yeah but" rather than listening and validating HER feelings.
Look, I'm not defending your XW here, because I don't think she's mother of the year either, just based on what you say, but you HAVE to know that calling your daughter a rat is NOT the way to smooth things over. And, you mentioned you have texts and recordings of interactions between mother and daughter....WHY? Not your circus, not your monkeys.
Let me say something about the situation with your gf as well. As I recall, your girlfriend is a good bit younger than you and you started dating and she got pregnant fairly quickly. I also seem to recall that you all didn't have the steadiest of relationships and that you were going to dump her when she first found out she was pregnant, but decided to stay. Your daughter is telling you, IN THERAPY, which SHOULD be a safe place to talk things out, that she feels like your gf was shoved down her throat and you explain it to us as she lied. Wolf, you have to stop trying to control everyone else's thoughts, feelings, emotions. While you may not think you pushed a relationship with your gf on your kids, your daughter clearly does see it that way and that is how she feels so you have to validate that rather than accusing her of being a liar about it.
You have a long row to hoe, especially if you are going to keep fighting to be right rather than fighting to do the real work that building bridges with your daughter will take.
Me 52, H53 Bomb drop 9/29/2014 Divorce from XH final 12/17/2014 Marriage #2 12/31/2019 5 adult (step)daughters (3 from XH's first marriage, 2 from current H's previous relationships) 6 grandkids