Most people would be a little paranoid after what sounds like an emotional affair. She fell in love with another man, and it caused drama. You did not push her to leave the home. She chose to leave.
Couple of things: she is not "permitting" or "allowing" you to do any thing. You are grown, accountable for your own actions, and you can do whatever you want without someone giving you that okay to do so. Your wife is merely giving her consent.
How long has it been since all of this transpired? I am not sure if you have forgiven your wife or if trust has been rebuilt, but those are other things to consider. You say that you are willing to rebuild the relationship, well, that means ripping off the scabs and being willing to reveal and ultimately let go of all the negative feelings to clean the slate and start fresh.
As far as you and the other man being friends, there is no rule that says you have to. Everyone has different opinions regarding that. At best, be respectful and maybe cordial. Especially if this man will be or has been around your child. Make sure to discuss what role that chap and any future people will play in the life of your child.
As far as dating, personally, I would hold off. Rebuilding a marriage takes work, and it is a constant work in progress. It will test you unlike anything else. So there is nothing wrong with meeting like-minded friends, but a romantic relationship may not be the best of ideas immediately. A lot of people here use OKCupid, and most have had success. From what I have read, they often link their partners/spouses and ID themselves as poly on their profiles. I have no experience with it, so I will let others guide you in the right direction.
Best advice: take it slowly, improve communication, learn how to talk with and not to/at one another, deal with your jealousy (plenty of articles on here about jealousy), try to understand that it is not a competition for her love and affection (Your wife saw something special in you that made her fall in love you and her need for more has nothing to do with you; you could be her idea of perfection, and she would still seek something more; no reflection on you. Continue being that same person she fell in love with), and voice what you need or are uncomfortable with. It is okay to have boundaries. Figure out what they are and work with your wife to find a reasonable, happy-medium. Preferably ones that will satisfy what both parties need.
Seek a poly friendly therapist. We see a psychotherapist who specialises in kink, non-monogamy in all forms, BDSM, and alternative lifestyles. It helped to have someone who was not thinking, "These godawful people are why the sanctity of marriage is royally fucked and on a steady decline."
Good luck, and I wish you well.