"until he has proved he is capable of a healthy, respectful relationship."
OP, you have to let go of this dream. You are not so special that he will give up everything that has worked so far for him just for you. And everything he has done with his partners so far has worked, for him. The evidence that he thinks this way is all in your posts. He treated you terribly, he left you for someone else, he treated her terribly, he was accepted back by you. He has had relationships with at least two women, one of whom (you) has borne him a child. He has had a roof over his head, meals, laundry and sex. Everything he has wanted and needed, including the handy human punchbags, he has got, just by being himself. His ego needs are a bottomless pit that no course can hope to cover over, let alone fill.
You are in many ways behaving like a child, as Dittany and so many others have said, indulging in magical thinking about this man, depending on your RL circle of supporters to pick you up when things fall apart, not seeing that your responsibility to your DD outweighs every other consideration now, but only seeing your life in terms of your own ego. Yes, ego. You believe you can change or control this man, if not now, then somewhere down the road. You believe he will do things for you and for the sake of your relationship that he has not shown any willingness or ability to do in the past. You believe your faith in him and in the power of your love will be vindicated, if not today or tomorrow, then maybe two or twelve years hence. This is the approach of someone who does not take responsibility for herself, and does not take responsibility for her child as a result.
You simply have to take that responsibility, OP. It's much harder than crossing your fingers and hoping things will magically change, believing he will change when there is no evidence, and hoping others will jump to your aid when the s**t hits the fan instead of doing the hard slogging emotional work to make sure that situation is avoided. This will involve getting to the bottom of your childhood, and learning to think like an adult in relationships, and like a parent regarding your child. This will be very hard for you if your own childhood lacked the security and emotional sustenance that are so important, but it is your chance to shape your DD's future so that she won't end up in the same mess you are in right now.
It is very hard to accept that none of what he has said or done to you has been meant personally, not the good and not the bad. All you have been is a convenient punchbag and a set of orifices that suits his anatomy. If it wasn't you, it would be someone else -- you've already seen that happen. He swaps women like some people change their socks, OP. One is as good as the other to someone like him. He does not see anything special about either you or the OW. The good thing about having two of you is that he can play you off against each other, so you vie for his favour, like children trying to get in the good books of a feared teacher.
I hope the breakdown you had doesn't scare you into thinking the devil you know is better than the uncertain and rocky unknown. Growth and strength sometimes come from unexpected experiences, when we are vulnerable and off balance. Don't try to preserve what you know and are familiar with, bad and all as it is, because the unknown is more scary than the familiar. The easy path downhill with fingers crossed is hardly ever the right one.