I've been in a similar situation as your wife, but seem to find the table turning a bit now. My husband and I are emerging from some serious bad spots in our 20 year marriage and are probably the strongest we have been in a really long time. I can only suggest keep trying to get her to agree to counceling, even ask her pick the counselor (you can always change if it's not the right fit). Keep talking to her, she was blindsided and needs some time to process her reactions to all this. This next year will not be an easy one.
My husband has done a lot of the SECRET online relationships and I did (still do) see that as a form of cheating and I suspect that your wife does too. This breach of trust is hard to get past, but not impossible. If I found out that he was secretly carrying on with someone online again, I would be extremely hurt, but if he came to me and said "I'm feeling the need to flirt online again" (or some such), I would tell him "Go Ahead, just keep me in the loop". I'm not sure he's ready to trust that I would handle it well based on our past, but I do mention it from time to time.
He does have a few very close platonic relationships that definitely go beyond merely friendship. It took me a long time to understand this and be OK with it. We are told over and over again how we "should" love and if we just love someone enough, we "can't" have these other feelings. It doesn't work that way, but it's a hard programing to break. When I discovered that I could be OK with this new way to view relationships, I realized that we are very similar in this respect, only I spent years pushing people away and keeping a safe distance from everyone for fear of letting people get too close.
Definitely spend some time getting to know your wife again and let her get to know who you have become. "The Five Love Languages" by Gary Chapman is an awesome book and should be read by everyone in a relationship. you will find your self wanting to slap your forehead and saying "Well that explains a few things".