I agree, making the final decision is difficult at best.
Suki has the right idea, break it down. Perhaps the starting point is to start looking for a job, even it is only part time, it is a start. Little steps that take you in the right direction.
Your children hear and see everything, although they may not comment, children internalize. Living in a home with an alcoholic is not a healthy situation for your children. I know, that was my life, I still bear the scars.
I can't tell you what to do, however, please make your children your priority.