Thank you for your question.
From the sounds of things, as you have outlined them, I do believer there is hope. Your relationship can definitely be saved. But of course, that takes two, and you are waiting for his answer. The good news is, that I see that you communicate and that you are still discovering things about each other, even though it took a crisis to bring that out.
You are handling this in a very mature way and it is critical that you respect the space he has asked for.
He is giving up a lot to walk away because he is not only giving up a relationship with you, but he is giving up a relationship with your child.
If his feelings for this other woman are so strong that he has to resolve them, then it is best the way you are doing it. You would not want to be in relationship if his energy is mis-directed to thoughts of her. You want him focused on you and your child, and your relationship with each other.
The only trouble spot, and I would not really call it a trouble spot, is your use of the phrase: "...I forbid him from seeing her last year". Perhaps you meant that you asked him, but if you really did forbid him, that is a small glitch.
In the course of human behavior, when adults are forbidden to do something, they likely will push back in some way, or act in a way that might sabotage the mandate. Hence in this case, a mental preoccupation with his feelings about the forbidden.
Ultimatums and orders do not normally work in relationship. What works best are special requests and respect for each other's feelings.
So at this moment, there is hope, and actually, a better than even chance that he will remain with you (and your daughter); but what is critical is how your respect for his feelings and time apart shows up. (plays out).