I need advice, but this is also partially me venting too.

Wife caught me emotionally cheating today. I'm not gonna lie, things have been very rough between us for the past few years. Dead bedroom. Sexless marriage. There was a random woman messaging me out of the blue. Very attractive. I knew what she wanted. My usual tactic of scaring people like this off, is asking them to send nudes. That has worked 99.9% of the times. I guess this was the other 1%. Because she did it. I was shocked, I never imagined that someone would actually do it. Then she asked for money. I didn't bite. But she kept on talking to me. And she did everything I have wanted my wife to do. Things that I've been asking her for years. Which is talking dirty and was willing to entertain my kinks in the dirty talk. And she was giving me attention. Which I was starving for. My God, it was so nice to get the attention , and to get it the way I wanted it.(even if it was just to get money out of me) And I got caught. It broke my wife's heart.it crushed it. I don't think there's any coming back from this. Even though she wants to work it out. She doesn't want to get counselling. But I've been asking her for years to get counselling and she has always refused. Saying that I wiI humour them, but not actually implement the necessary changes. She is justifiably angry and hurt. But I've been telling her for these past 2 years that we really need to work on our relationship as a couple. Which is part of being married. I keep on saying and saying it. And she always dismissed it. I finally slipped. And i got caught. I know that there's no coming back from this. I live in Ontario Canada, and I wish to get an amicable divorce via arbitration. I am willing to concede whatever she wants. In order to keep it amicable. Because my parents were locked in a lawyer battle for years. Because they were too stubborn to let go of things. How do i go about this? Who do I talk to lawyer wise? We have kids, and I want to have shared custody. At the very least, I want to be able to see my kids. And spend at least a little time with them. I don't have the foggiest idea how to go about this. But I know that in my heart of hearts. It's over. I think she knows it too. But is in denial. How do I do this guys??