Could you be diligent about pulling up the grass that is popping up? I've poured boiling water on weeds too. Or add more mulch on top of the places where grass is popping up? It makes me uncomfortable to spray vegetation killer where kids play.

Don't spray it with chemicals. You may have to add mulch periodically since it does decay and kids naturally kick it out of place. Keep it pretty thick (4 or 5 inches). Pulling weeds is not that bad if you just keep an eye on it and develop a habit of plucking them out as soon as you notice them. Show them to your kids and explain what you are doing - they can and will help. (Payment of a penny per weed helps.) Boiling water really does work well. Just out of curiosity - did you choose mulch instead of grass to avoid mowing?

I would suggest using plain old Roundup. It is one of the safest chemicals available (if anyone disagrees, do the research like I did) becuse it degrades naturally after exposure to sunlight or after a very short time period.

I second the Roundup if you have an abundance of weeds. You can always time your applications for say, the night before a rainy day, so that the residue would be washed away before being played on again. Good luck =)