Dear Why...
I know this will hurt you, but I think it's the only way you might have a chance. You need to take away what she is used to getting from you, stop pampering her.
She knows that you will always be available... but turn that around and be available only for couple counseling and whatever you two have to do for the children. Demand regular time with the children so that they will feel that you are a steady part of their lives.
You don't however, need to assure her of your availability for HER. As a matter of fact, you should try and be as 'cool and collected' around her and don't give in to her manipulations.
When you deny her, you are letting her know that she has to make up her mind to either try and work on loving and trusting you again, or to plan on being a 'divorced family'.
You are a human being, not a monster. And the mistake you made is a forgivable one - and you need to start by forgiving yourself. I'm sure that you are also willing to forgive your wife for 'cheating' on her new boyfriend and you, so don't you think it time for her to forgive you?
I hope, for you, that you can stand strong while she is growing up.
So, for now.. keep your body and emotions from her so that she will have time and a chance to miss them.