" I want me to be happy and my children to be happy"
Are you happy now? You surely don't seem to be. I know you feel only one thing is going to make you happy, but you know what?
You can't have it. Right now, or maybe ever, you cannot have the only thing you believe will make you happy. And you aren't happy now.
So, I would find a way outside of your W to make yourself happy. Else you'll be miserable for the rest of your life.
Fear keeps you in paralyisis mode, but I don't think you realize what you fear the most has already happened. She's gone. She may be physically there, but otherwise she is gone.
Sorry to be so blunt. But your M is over. What can you do to build a life for yourself for you and your kids?
THAT should be your only focus right about now. Not an ounce on her.
I'm afraid you won't be able to move on being in the same home with her. But she isn't going to move out especially while you live you separate lives in your home together. But she has left the marriage, not the house.
I hope you find a way to find happiness outside of your wife. I hope you come to accept one day you cannot have what you want in regards to your wife. So you decide to find your own happiness.