This man has checked out of your marriage and is not your friend never mind your partner in any shape or form. You need to protect yourself and children financially for what is to come. Draw everything you can from joint account and keep it safe somewhere. Bills have to be paid and as he is undoubtably having an affair, his priorities are totally elsewhere. Get the bills transferred into your name. This is a joint account you have an equal right to manage it.
He left and then came back out of guilt but couldn't settle. Affair may be ongoing or OW has given him an ultermatum to leave you for her which I suspect he promised her a while back at same time as he was being awful to you. He is being totally predictable.
You must be the opposite. Gather his stuff, tell him to collect it from outside the door. Minimise contact, no needy/ begging calls/ texts. He will use each one against you at the moment. Read up on doing the 180 in relationships and act as though you are fine, can manage perfectly well without him and keep acting until this is normal. Put one foot in front of the other and hold your home and family together. You've got this.
Avoid alcohol it will merely make you emotional, indulge in some you time - long bath, sorting your wardrobe out, getting hair done, drink with friends/ outing with children, trip to something you enjoy. Just carry on and soon you will feel calmed by the routine. Give off an air of indifference and disinterest when he contacts you. Do not ask questions. He will be expecting you to be a cling on, don't give him the satisfaction.
Think about all the negative behaviour you have had to endure from him over the years, think about every single controlling behaviour he has exibited previously, every put you down. You are free from all this now and will manage.
You owe it to your DC's to be their rock and safety net. Plaster a smile on from morning to night for their sake. As a mother, if you have gone through labour there is nothing you can't endure. You've got this!
When the dust has settled, see a solicitor, find out your rights and even consider filing on line to save money. Very straight forward these days.
Thinking of you OP. It is a frightening time but one you will get through.