Hows it going buddy? You sound like your struggling.
You are not "sitting there rotting away", you are stuck. This was such a blow that you had your legs knocked out from under you. You will stay stuck until you have grieved enough for the loss of your marriage. Then, when you accept your situation, you can move forward.
Solo, my marriage seems over. I accept it. I hope that my wife considers remaining in the marriage. I learned this week that waiting is a form of pursuit. So I'm no longer waiting. I am living my life. I've have made new friends. I miss my wife but shes not there.
When you feel ready to get on with your life (finish grieving), get yourself up, brush yourself off and live. I am so busy doing what I want. What are you doing besides working? You need to to keep busy. Can you go out with one of you kids? Rotate through them and give them one on one Dad time.
What I learned is this. While I was grieving I was miserable. As I was in mourning for my marriage I posted here and went to meditation. During this phase I grew to accept my situation. I am no longer the walking dead, I have joined the living. Life gets easier Solo but not till your ready.