He has left the marriage, so all you can do is let go and begin a new life. This is a very emotional time for you on many levels, so I would try to keep daily life as simple and ordered as possible. The only obligation you have, after the funeral service is completed, is to your children and yourself. It is a time of mourning, a time of reflection. So try to keep stillness and order in your life in the coming several weeks as much as you can. It will help you heal from all this hurt.
When something is destructive to our lives, all we can do is get away. And sometimes the person we must flee from is our spouse. You are facing reality and taking action, which is what mature and reasonable adults do. And your children need that kind of mother.