Tell your father what you found. Throw the ball back into his court; this is something for him to deal with, not you.
While you shouldn't have gone snooping after you saw the first email (you should have come to him then
), what's done is done. If he opened up his email to you, then he had to have known it was possible that you would find him out.
Here's your script.
Dad, when I was looking through your emails for ___, I found intimate email conversations between you and men that went back to 2009, and those included information about meetings.
Have you told Mom? Because I will have a lot of trouble keeping this secret from her, and I will not lie for you.
I am also concerned about you, and I hope you are being careful with your health. We all love you and want you to be around for a long time.
And see what he says. He might beg you not to tell your mother. In that case, you've made it clear; you're not going to lie although you might slip up. It also makes it clear that there's a possibility that you might err and share this information with your sibling.
He might claim he's already told her. Then in that case, you can say that you might mention it to her on occasion but you won't be bringing it up as dinnertime conversation. In that way, if he's told her, then fine. And if his claim is a false one, and he hasn't, then he will if he's got any sense.
Ending your talk with concern for his health and affirming your love for him is important. His secret is out, kinda, sorta. You need to assure him that he's still your father and that you still respect and care for him. But you are also mindful of your mother's future health (and his as well).
This little speech should cover that. Ultimately, this is between your parents, and you should never have been made a part of it. But you are right now. They may not see it as cheating; they may have an open marriage and just see this as a part of it. You don't know what really goes on in their marriage, despite your "best friend" status with both of them.
Do your best not to judge their choices, okay?