Tom, my baby sister is in AA. She insists we should all just try to do the next "right thing". I trust you to protect your kids and value yourself.
I know you are at a low spot, but I assure you that you will cycle out of it because you are capable and willing to take care of yourself. Some day you and I will meet up and laugh about how awful some of this was...
Keep your plan to send resumes. Consider temporary agencies for in-between... You are so smart... lose the fear. I will too.