The problem is he tells me "I will quit if you stay. If you don't stay, I'm not going to quit." So that tells me that he doesn't want to quit.
You stayed and he used anyway so don't let words trap you or make you feel guilty.
Do what is right for you and your children. Staying with an active addict (and regardless of what he says, he is an active addict) is dangerous for all of you, presents a terrible life for the children and obviously makes you very unhappy.
My son was a terrific fellow at one time, kind, handsome, good natured and funny, everyone love him. Addiction took that person away from all of us and all the wishing in the world won't bring him back.
Take a good read around here, especially the sticky posts at the top. There is lots of good information there that may help you through these troubling days.
Welcome to SR, you are among friends who understand.
Hugs