First step is to get legal representation! You must protect yourself and your kids. Do not just trust her to do the right thing.
The Divorce Remedy book explains the LRT. Several newcomers use the term "going dark" but I don't think some may fully understand that concept. It is almost impossible when co-parenting. However, you can use the LRT, and should, b/c this is the last resort!! She wants a divorce, so if you are ever going to implement the LRT, it's now.
Have you followed the 37 rules? Have you read the first three threads on WW's? If so, does it sound like your W? If you suspect an EA, then I suspect she has shown some similarities of what I describe in those threads.
You say you know things could be awesome again. People cannot become awesome in just a few months. Sorry to burst your bubble. Do you have a plan of action to turn yourself into an awsome man, b/c that has to come before an awsome M. It takes very hard, consistent dedication to change yourself into a better man..........and that's just your side. It doesn't begin to touch the process she has to get through. So, it may, or may not, come after the D proceedings.
I understand needing hope. Looking for signs in her, as matter of hope for you will a waste of valuable energy. She will play you like a yo-yo. Maybe that is not who she use to be, but it is who she is now. If there was no abuse or legit reason for her suddenly leaving and pushing for a fast D, then I would take a bet that she has her eyes on another man.
You asked for steps. Read the WW's threads.
Let me ask you something. Even though you are separated, how much do you think she's worried about losing you completely out of her life? Would she think you would be available as a friend, or whenever she needed something?
Have the two of you had some type of contact every day? If so, this needs to stop. Don't use the kids as an excuse for contacting every day. People can work around it. Has she even had time to miss you? My guess is "no".
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!