If you can afford to pay for child care when there is no school then find a nearby child care center and get on the waiting list ASAP. According to BabyCenter, child care costs range from $4,388 to $14,647 a year. If you can swing it, you'll be able to work easily while they have no school.
Ask family and friends for help. Sometimes you just have to ask in order to get the help you need. Even if it is just once a while, you can get some work done during that time, and the kids get to spend time with their relatives and friends.
Keep them busy. Have a stash of stuff to keep them busy if they have to be home. This should include their favorite movies, board games, arts and crafts, and toys. Take one out at a time and it will keep them busy until they get bored with it, and that's when you give them a new activity.
Spend quality time with your kids. I have found that if I commit to some quality time with my kids every day, then they are less likely to bother me for attention while I am working.
Take your work outside with you if you can. Take the kids to the park or just outside in the yard. Work while they play and get some energy out.
Buy them a computer of their own and allow them some computer time. This will keep them busy while you work from home. Plus, they will need a computer for school.
Take a trip to the local library. It is usually free and you can bring your laptop to work or do research while you are there.