He is a coward through and through just like my ex. Mine actually did the same thing. He blindsided me and moved out of our new home because he didn't love me. I asked a million times if there was someone else and he continued to say no. Turns out, he was banging his own secretary and is now living with her.
All I can tell you is that these people are not normal. We look at these issues with our rational brains and they make no sense whatsoever. I think they fly by the seats of their pants, don't think for a moment and block out all thoughts of consequences. What is cruel and annoying is that they take charge of nothing. They can't tell the truth about it so they are like two year olds - if I don't acknowledge it, it's not really happening. I would have been just as hurt, but I may have had an ounce of respect left for my ex had he just said it. Had he just sat me down and told me the truth. I figured I deserved that, but I guess he didn't. He wanted to eat as much cake as possible at mine and my children's emotional expense.
When you finally find out the truth, I think it will bring you peace. It will hurt, but it will no longer make you doubt yourself or your capacity to be loved. You will know that he was a cowardly scum bag all along and that you weren't the crazy shrew of a wife that his messed up brain wants to see.
As far as your DD meeting her, if that ever happens, that will hurt too. I knew it was going to happen, so I prepared myself as best as I could, but it still kicked me in the gut.
All i can say about that is that it gets better. I dont know how or why, but it does. Its like you somehow become numb to the hurt after a while.
It's an unfair steaming pile of shit that these POS OW get the benefit of time with our children, but there's nothing we can do about it. Just know in your heart that you are the one and only mother they will ever have. You can never, ever be replaced. Also, know that a shallow, selfish twat who sleeps with a married man who has two babies will eventually show herself as a shallow, selfish twat. She might put on a bit of a show in the beginning to try to validate herself and make her place with the kids. She won't hold a candle to you, ever. She's simply the price of admission to see their father. They might accept her as part of his life, but they know full well the difference between her and their mother.
Just brace yourself and practice your fake grin and best "that's nice" you can muster if they ever come home from a visit and talk about her. I always found it helpful to have a relative or friend at my house with me when they got home. Its a distraction and someone there to be by my side if they told me something that i found hurtful or upsetting.
I know its hard, but try not to spend too much time worrying about it. It's just one more part of this shit storm that we can't control.