Check laws for your area, consult an attorney about your options.
If you have proof of affairs or abuse use it. Document everything. Go from there when/if you talk to a lawyer; which I do encourage

I got a divorce in georgia. The only difference was I hadn't seen my ex-husband for 4 years prior to filing. I met with the lawyer told her the situation, turns out it was abandonment I paid her half of the total amount as well as gave her his last known information and she did the rest. Once everything was done I signed the divorce papers/separation agreement and child custody agreement. He waited over a year to sign and return his but it was finally finalized.

Well first thing maybe leave take the kids one day when he’s gone go to a women’s shelter and have them help you get resources and go from there or he might take off with them and having no money won’t help but at least if there with you he won’t find you there if you tell them the situation get child support right away