Red, great, you are not moving in yet. Please use this time to work out what you want and think.
I'd personally be telling him it is not a done deal yet, give him a real reason to change. Tell him you are still considering; if he can change plans, so can you.
Will he get the therapy in the next month, one, two sessions or more or none? My guess is none, just see if he does....
Whatever your reasons for therapy I wish you best luck with it.
"...felt that I went straight in from the first session and opened up massively." that's the idea, really it is, she can't help you if you do not open up. If you are used to keeping your cards close to your chest this will be a challenge. BUT it will be worth it.
"I didn't tell her about the incident when he was aggressive (it was just one isolated incident and I split from him the next day) because it seemed almost irrelevant at the time to my current issues. I wanted to discuss it at a later date as we continued to build trust." Then do it, she knows it is on the cards so talk to her about it and ask her why she is worried.
Maybe, now is the time to tell her, maybe you need to allow her to see these things. Please also remember as you think about this one incident, you split from him because of it. You have no idea if there would have been more, I am guessing there would. But you had the chance to split, the courage.
Allow this courage to surge through you as you move on with your life.
Please do listen to 53rd she seems to really understand where you are coming from, and your situation.
In real life I have a friend who is in a similar situation as you, in real time. Her ex made a grand gesture and seemed to be doing much better, then suddenly it all slipped, he is not stable and suddenly it all comes to the front.
I really worry for her, she has several kids and they are all dependent on her, just as your dd is on you. Yet she seems determined to centre her ex instead of the kids.
I hope so much she will see a way ahead that will centre her and her kids.
"We were from the end of Feb texting regularly and hiding it pretending we weren't getting back together."
I am guessing this may be a bit exciting, like having an illicit affair? Not that I would know about either situation but I can guess. Maybe you are feeling special, you've got a secret that no one knows for sure, not even the anonymous people on Mumsnet are completely sure what is going on!
But the reality is, he has not done any of the things he said he would, not sustainable, not yet. Once bitten twice shy. Be wise, you are playing into his hands and you know from experience that is not a good place to be.