Seems you both hurt each other. The 'why and how's' seem kind of trivial now. Why don't you try to approach it as a 'new affair' or 'new relationship' with her? A clean slate for the both of you.
BTW, don't you think that maybe your infidelity was more revenge than to make her feel less guilty?
"It is curious that physical courage should be so common in the world and moral courage so rare." -Mark Twain
