I think you two need counseling.

Your wife was wrong to imply your absence of any kind caused her to be unfaithful. She is responsible for the wrongdoing and honestly, has she asked for forgiveness for her actions? Has she admitted she did something wrong and needs help? Has she discontinued the "catching up"? To what extent was the emotional affair? Was she "sexting," cybersexing, sending nude photos, etc.? I'm sorry to be so crude, but I've heard of other situations where there was no physical contact at all, and a spouse found out about their husband or wife sending nude photos and cybering and considered it cheating.

I can't advise you on whether or not you should leave, but consider the fact she may revert back to this behavior. Also consider whether or not you're prepared and want to handle a divorce.