As far as responding to your wife, I'll give you the same sage advice that was given to me when I first came here - validate, validate, validate.
She doesn't need to hear an argument for why she should give you another chance. What she needs is to hear you validate her experience. For you to acknowledge how difficult those years must have been for her, when she was trying to get through to you. Acknowledge how it must have hurt her when you left giving her the ILYBINILWY speech. Acknowledge that you are sad that it has taken you so long to realize what is important to you and you understand that it may be too late.
Even when you don't agree with her interpetation of something, it is still possible to validate her experience - saying something like "I'm sorry that you had that pain, I never meant that to affect you that way" or such.
Also - pay attention to actions not words. She may say a lot of stuff to distance herself from you - the first clues that she is softening (if she does) will come from behaviors.
And - focus on the kids and on being the very best dad ever. It will impress her and even if you don't reconcile, the relationship with your kids is the most important thing anyway.
