D.,
I'm so sorry for your situation. You are very brave for taking the steps to end a sour relationship. I'm not going to ask about what you've tried to do to reconcile as I don't think that's the advice you were asking for. I'll be honest, though...
My Mom left my Dad when I was 2 and my sister was 3 months old. That was 32 years ago and my Dad became a dead-beat Dad and left the state. My mom had very little child support throughout our growing up years. Selfishly, it was hard on my sister and I not being able to have/do the things that everyone else did. My mom had to work two jobs to make ends meet and NOW tells us stories about how she had $5 left over and had to figure out how to feed us. BUT, on the bright side...she did it. She worked hard and most importantly, built up a network of support. We lived with my aunt for sometime, my grandma/grandpa and one of my uncles. The loss of your mother to cancer won't make it easy (for the obvious and unobvious reasons). Do you have sisters? A brother? A best friend or some close friends? Talk to them, be honest, be open and ASK FOR HELP. I'm so thankful for the time we spent with my mom's best friend when we were younger. You are going to have to rely on people you know and trust to help you with your kids.
Then, there's the father. He has a responsibility, too. As soon as you can, TALK TO AN ATTORNEY and get something filed with the state that will assure child support payments for your kids and visitation for him. No matter how "friendly" your split is right now, don't think it will always be that way. Trust me on this one...my mom took the "I'll work it out myself" route with her last relationship (14 years together) and it's been a headache ever since.
D., good luck with your life-choice. Although the road may seem hard, I can tell you with 100% certainty that my Mom's hard work, dedication to us and independence made both my sister and I very strong, independent and successful women.
T.