It’s a common problem. It is naive to think this cannot happen to anyone.
I went through same situation as you. Parents cheat and they do mistakes, some times they realize what they did and seek forgiveness. My parents reconciled after such episode happened 22 years ago, when I discovered my father’s relation,
It took a heavy toll on me for almost one year, like crazy. But we went back to normal, I moved on like it never happened, he loves me no matter what and I’m absolutely happy for every moment i spent with him.