Please don't feel guilty for making a "mistake". You fell in love with someone and wanted to make a life with them. There is nothing wrong with that. It's not working out the way you'd hoped. But it takes two to make it work and if he is not living up to his responsiblities as a husband and father that is not your fault.
I understand that you don't want to leave because of your children. But please think about the flip side of that - your children can be damaged if you continue to stay.
I am the child of an alcoholic. I had a solid, stable mother and extended family while growing up. But I never connected the dots between why I was choosing partners that could not take care of themselves or had "issues" until my last relationship which turned out to be with an alcoholic. I am now 39 years old. It has taken me this long to make the connection between what I experienced growing up and the choices I am making as an adult.
My father has been sober for 20 years now. He's a wonderful man and has tried very hard to make up for the chaos he caused when we were children. But nothing can make up for the dysfunction I learned and nothing can make up for all the years before I recognized what the issue was about.
Please think very hard about what you want your children to learn.