norks, I've been there. Don't be so hard on yoursef!
You don't have to socialise if you don't want to, on the other hand much of your analysis of everything will occur when you're alone and it will at times feel overwhelming. It is progression although it might not feel like it right now and it is hard but will become easier.
Your Dsis's 'moving on night' was no doubt a well intended idea, she and your friends obviously care very much about you but moving on is not something you or they can force. Don't feel bad that you are feeling bogged down, that is totally understandable!
You can and will look after your children no doubt! This is where you could encourage your friends and family to help out. Directing them to things you feel you could do with a hand with, will be far more productive than them doing whatever they assume you need.
Regarding the children and practicalities, take small steps to make your life easier. Quick, easy meals are fine for now, sending a bag of washing off with your Dsis, doing weekly shop online are all the kind of things which can make living a little less stessfull in the earier days.
Your emotional heath has taken a battering and needs to be given the same allowances and care that you would give your physical body if it was bed ridden. You will make it through this norks, not least to make absolutely clear to the philandering oik that he made one helluva mistake but more pertinantly, because you and your children deserve a future and more so, a happy one.