YOu have got some great advice, can I also add that you must go back to the debt management company or (better) one of the free debt management charities (CCC or Payplan) and tell them you cannot manage. You must get these horrendous debts under control before you can even begin to rebuild your marriage/family life as they are basically the stress that is corroding it. I'd also point out that you need to check that if you work, it won't just be poured into your debt. My life is 10000% better now we have a good and regular debt management plan in place, and it has allowed us all to calm down, seek more and better paid work, enjoy each others' company.
If your husband is saying 'I don't know why we had children, everything was ok before then' (which is not what he actually said but this is what you believe), this is just an expression of his extreme frustration and stress of being in debt, having three girls to depend on him, the knock-on effect of having cancer, and of seeing his wife also struggling with alcohol and stress herself. He must feel terrible and is probably suffering from depression/anxiety too which will impact how he interacts with the children. I very much doubt he really hates his own children, more likely he hates the circumstances you are in right now and blames himself for them.
I agree with whoever said you have to stop putting your energies into blaming each other, and start putting them into being a team that drags each other out of this mess. Stop criticising him, he's actually not cracked up and continues to work in very difficult circumstances, you've also held it together with the children. Get the debt sorted out so you are not scraping by and that will be one big worry off your mind which will allow you to relax a bit.
I get the impression you were hoping he would agree to leave just to solve the problem, I very much doubt he will. And, really, I cannot see it helping anyway, given you have a strong relationship between the two of you and your debts will not vanish. That is definitely a basis for continuing rather than jacking it all in in some desperate hope that any change is good change.