Best of luck to you. I am in the same situation. I have two kids, a 5 year old son and a 2 year old daughter, plus I work, go to school and my have own workouts, usually 6 days a week. For myself it meant getting into a strict routine. I work part time at a gym, in addition to my full time job, 4 hours a day 4 days a week. So the workouts are easy for myself. And being an employee I am able to use all of the equipment for no charge. Which is nice being money isn't growing on the trees in my backyard yet!
Check around your area, see if there are any gyms that are open late or very early. That way maybe you can go when they are still sleeping, and it is ususally easy to get a sitter for 2 sleeping hours. Depending on your work schedule.
The idea of child care at the gym is also a great idea. Kids always love to play with others. Or maybe it is possible for you to do some of your workouts at home. For myself, my kids love it when I workout at home. Plus you are promoting a healthy lifestyle and the importance of taking care of yourself. My kids have their own dumb bells, 1 and 2 pounds. But they say they are also "working out".
Good luck to you!