That all sounds very awful, your world has been flipped upside down. It's going to be hard for awhile. There is no perfect answer that is going to make everything better.
Right now, one of the best things to do is breathe. Then try focusing on one of your senses for about 10-20 seconds. Calm your mind and then be present in the moment.
You are going through grief and loss over the relationship. The children are too young to truly understand what is going on but they know that you are not okay.
Remember they need you. You are their rock. When they are older, they might not remember specific events taking place now, but they will remember the feeling of the emotions. Focused on one moment at a time.
I was exactly where you are. For months I walked around with a knot in my stomach. I wasn’t interested in anything. I had to use sleeping meds to avoid waking up and running over everything in my mind. I don’t know if you have considered antidepressants but they can help get you through to the other side. It will get better. I know you don’t believe me. I didn’t believe others when they told me that. I’m on the other side of the depression. I’m still going through the divorce but I feel like myself again. There are people out there who are rooting for you.