I was a single mom, with no family nearby and had to pay for every minute of childcare when I was working.
Ask around your friends and see if anyone else lives near to you and has kids the same age. I managed to team up with another mom for a while, who lived in the same street as me. We both worked at the same hospital, and manage to set our schedules so that we worked opposite days, and the mom who was home had both kids. She worked Monday Wednesday Friday and I worked Tuesday Thursday Saturday, all 12 hour shifts. It makes a huge difference when you have free childcare, and your kids enjoy being with others as well.
Also, figure if you can manage without a car. I've never owned one, I've always chosen my jobs based on transit options, so that I can get a bus or train to work, and ride my bike in the good weather. Not having a car payment, gas, insurance, etc makes a big difference. I currently pay $100 a month for transit and thats it, no other travel expenses at all, and my hospital has a scheme where transit is paid pre tax, so I even save on taxes too!
Meal planning can also help to cut costs. Plan a week of meals, then convert the recipes to grocery lists and go buy it all for the week. Make double portions of meals and freeze the second one to use the next week. I make soup in large quantities, (Panera recipes are online and they are great!), and you can freeze it into tupperware pots and just take a couple of pots out the freezer each day.
Living with kids on a budget can be done, but it takes planning and organization. Sign up for netflix instead of paying for the movie theater, and cook your own popcorn!