For gods sake stop doing his washing, stop cleaning up after him, stop cooking for him. Put him in another bedroom or on the couch, make his life hell.
THIS ^
Do NOTHING for him.
Doesn't want to be a "weekend dad"? Well in that case he should be treating you with respect and either working to repair your relationship, or moving out so that his children can stay with him part of the time - perhaps even more than the weekend. But of curse, he won't want that because it will spoil his image of himself as a wonderful father, and also it will mean his style is cramped if he wants to bring someone home.
You are worth more than this.
Your children are worth more than this.
At the moment you are still reeling from shock and despair - toughen up - when he comes home tonight let it be to no meals. Let him find his belongings in the spare room, if you have one, or in bags/boxes behind the settee if you don't. Leave his washing and ironing for him to do. If it piles up - tough - DO NOT DO IT! No SEX - so many of these men think they are still entitled to a stage when they feel like it, and their poor wives allow them because they hope their useless husbands will reconsider their decision. YOU go out any enjoy yourself (or go to a mate's house and weep your heart out. Let him feed, bath and read a bedtime story to the children. Work out which days he is looking after your children (from breakfast to bedtime) and which days you are; which are his weekends off and which yours. Just because he is present in the house it doesn't mean that he doesn't have to step up to the plate. After all - he doesn't want to be a "weekend dad". You can take it further - which nights are his nights to choose what's on the telly, and which nights are yours etc. He doesn't get to just do what he likes while you sit at home with your children.
And even if you don't go out - make him do his share. Don't let him get away with ANYTHING. He is a twat - but you don't have to be a doormat.