PA: I would look into getting emergency spousal support and child support first of all (assuming he's working). Close all joint bank accounts and joint credit card accounts. Get Legal Aid if you cannot afford a Lawyer or call your nearest courthouse for help. Since you said you know some things like yoga, etc., see if you can get work teaching a class in one of these areas and have your husband, friend, another mother or family member take care of the kids. It takes time to heal from a separation/divorce. I went to the local Food Pantry and shop at Thrift Shops and drive an old car. I've had plenty of time to think.
While I understand the desire to keep all the details to oneself and to feel embarrassed or ashamed at one's marriage ending it is also true that you will need the support of the others in your family and community.
If you have told no one the reasons behind the divorce then it's time you did so. I was petrified to tell anyone and was happily surprised at the support I received when I did. I also talked to them about what I'd like them to share with others. Yup, I gave them permission to talk about me.
This helped to spread the truth from my point of view instead of everyone only hearing what he had to say. There were a lot of people with a lot of questions and this way some of them were answered. Later on, when I felt a little less vulnerable and raw I was able to talk to them about it.
But silence. It's a void waiting to be filled and it'll be filled one way or another.
As busy as you are is there any time for counseling for yourself? Hope so. It may help you with the whirlwind you're in.