We can all get into a mess in life, for many different reasons. we're all weak, in parts, and things can spiral out of control.
BUT when there are children involved, when children are sucked into the mess, then that is a different story. You say that you 'begged' your husband to leave - why did you beg him? Why did you put the responsibility of the future of your relationship entirely in his hands? You didn't want to make that decision yourself so forced it on to him: he wouldn't comply, you gnashed your teeth that he wouldn't do your job for you. Meanwhile, the children were present, living in this shit.
You do not say that your daughter overheard the exchange between you and your husband, you say that she reminded you of when you said it. Why was she party to that conversation? She should not have been. I wonder if conversations, exchanges, of this type are common parlance in your family life. It is unacceptable to involve children - your children, whose job it is for you to protect - in exchanges like that.
Also, why are you only now seeking therapy to address this appalling and protracted mess? Why wasn't this done, say, 10 years ago? Why now, when the situation is so entrenched, so desperate, that you recoil from your husban'ds physical presence and incidental touch? That situation is POISON for the children - your children - who are forced to live in it. they have no choice, you are supposed to be their security but you have presented a family life, their only family life, that is toxic and profoundly insecure.