I've directed both older children (11 and above), adults, and mixed casts. Here are some thoughts about kid shows based on my experience.
-- The kids will memorize their lines (and everyone else's as well!) so quickly that it will make your head spin. I've directed some 60-something's for whom I've had to assign a back-up -- someone else on the stage at the time who would take a line when those senior moments hit -- but it's never been an issue with kids.
-- As a parent of a kid in drama, I emphasize this: whatever schedule you come up with, put it in writing (along with every other "rule") and make sure it gets into the parents' hands. They are the only ones who know the family schedule, and they are the ones who have to do all of the transporting. Do no rely on the kids to convey the information -- ask for a signature from the parents. Also, let the kids go at the promised time -- we hate to have to sit in the parking lot fuming.
-- Kids have a hard time standing still on stage. They tend to want to step forward on every line and to wander for no reason. I've resorted to threatening to put glue on their soles -- never have, but have been known to stop even tech week rehearsals by shouting from the house - why are you moving?!? Maybe there are some theatre games out there that would help prevent this problem ...
-- Consider banning parents from rehearsals. Although they are well-intentioned, they sometimes will "coach" at home, and you'll end up with an actor who has artificial gestures and inflections, and who doesn't know whether to do what Mom says or what the director says. Include something about that in your initial note to parents.
-- Establish your ground rules early and stick with them. Noise, running around, bringing friends and food, what's an excusable absence, etc.
-- Scheduling can be hairy because you'll have to deal with athletics, lessons, confirmation classes, and working parents. Cut your cast some slack early on, but let them know at what point in the rehearsal schedule the show must become a priority over other activities.
-- Spend some time at the beginning teaching basics: up and down stage, left and right, cheating, crossing, countering crosses, not telegraphing, projecting, the fourth wall, etc. It's fun to introduce concepts which we take for granted.
-- Expect a lot of energy which you can capture and focus. Stage games can help.
-- Although some of this sounds dire, you'll find most kids are fun to direct. They'll let you direct them (unlike many adults) and you can have great fun modeling your expectations. If possible, have another adult you trust work with you -- one of you then can work more closely with the kids who need more help "getting" it. I'll take a good kids' show over an adult show any day. Have fun!!

One thing that I've noticed is that a kid's attention wanders like nobody's business. If a kid is not being dealt with directly at any particular moment (i.e., you're not actually looking at and talking to that particular kid), then he or she will very happily wander off and go do something else in the middle of a scene. "Staying in character" is completely foreign. There's almost always someone who thinks you cast them as the villain because you hate them and think they're evil. And if anyone is supposed to be dead for any length of time, they have about 2-3 minutes (at best) of staying still in them before they start wriggling and squirming. This is all in rehearsal; usually by showtime they know what's expected of them and they behave. That said, kids have twice the energy and three times the enthusiasm of any adult I've ever seen, and generally make (for me, anyway) the process a lot more fun.

Remember, though; if you cast a kid, you cast their parents as well. If the kid's mom is absolutely determined to come to rehearsal, then there's really no practical way to keep her out without losing your Danny Zucco a week before curtain, especially if you're dealing with younger children.