I've got a 6 yr old and a 2 yr old, both have been camping since they were little (6 mos. for one and 3 weeks for the other). A lot good advice has already been posted. Here's what's worked for me.
-Keep it simple and cut back on gear. If you are frustrated because of the amount of time it takes to set up and break camp, it ruins the trip for everybody. Although we have a ton of gear in our storage closet, we've cut back significantly over the years as far as what we consider necessary. For example, even though we have 3 tents that zip together into a gigantic 10 person compound, we've found it plenty comfortable (and a ton more practical) to just cram all 4 of us into our smallest tent.
-Just because you packed it, doesn't mean you have to set it up. When I get to a campsite, I set up my tent, put the bedding in it and that's it. I keep all the luggage, cooking gear, etc in the back of the Jeep. We change our clothes and cook our meals at the back hatch of the Jeep and then put it all right back as soon as we're done using it.
-Prepare as much food as you can at home and freeze it. I practically refuse to cook anything when I'm camping, I merely reheat stuff that was cooked at home. If you freeze things in gallon ziplock bags and lay them flat in the freezer, you end up with a bunch of thin 12" x 12" frozen squares. These are very easy to pack into a cooler and will warm up very quickly on the stove. For certain meals (mac n cheese, stew...) you can even break off small chunks and heat up just one or two portions at a time. Use bagels instead of bread (doesn't crush). Collect single serving condiment packets every time you buy a hot dog from a gas station, use them camping instead of bringing bottles of ketchup, mustard, etc. We even did a full Thanksgiving dinner one time (turkey and all) by freezing everything into disposable buffet pans. We used rocks to suspend the pans over sterno cans. It took about 30 minutes to warm up our entire Thanksgiving dinner and we didn't have to tend to it at all. We threw rocks in a nearby stream and played in the sand while we waited for dinner to warm itself. Be creative, do anything you can to make your meals quick and easy to prepare.
-Figure out your kids' breaking point with respect to being couped up in the car (for my kids it's about 3 - 4 hours) and stop BEFORE that (I stop at 2 hours). If you let them out before they go nuts, you can make your stop shorter and they are easier to get back in. Combine gas stops with potty/play/snack/meal etc. I like to drop my whole crew at a city park with some snacks or their sandwiches, then I go get gas while they play. When I come back, we play another 15 minutes and then everybody's ready to hit the road again. That also keeps them from nagging you to buy junk food at the service station.
-Buy $5 worth of toys from the dollar store. Keep them hidden. When the kids get restless, break out a new toy and you've just bought yourself an hour or so of peace and quiet. If you're traveling Southern Utah (or anywhere sandy), bring a small bag of beach toys. The kids can play in the sand at camp, off the side of the trail, anywhere you stop pretty much, and they'll be less prone to wander off.
