Quoted:
Whatever equipment you get .. set it up and operate it at home first.
solid advice. learn how your tent/pop up camper sets up so it doesn't take you half an hour reading the directions and getting frustrated.
Shelter: I would suggest simple, two pole tents. The more poles, the longer it takes to set up (and more difficult). I wouldn't spend the money on a pop up camper unless you are planning on using the crap out of it for the next few years - most of the time it is a waste of money.
Sleeping bags: consider the temperature in the forecast for your camping area. No need to pack a 0 degree bag if it's going to be 50 at night, and same goes for the opposite - no need freezing your balls off
Food: Keep it fun and simple. Hot dogs, hamburgers, etc are good. Get some Mountain House packets and a way to boil water easily (single burner camp stove). Bring a small propane grill so you can grill hot dogs or burgers if there is a fire ban.
Water: bring at least a 5 gallon water jug with you, and refill often (may want to bring a filter/method of purification)
Clothing: keep in mind you won't be able to wash your clothes unless the hotel has a laundry room
Sanitation: bring a bucket to poop in, unless you know you'll be near a bathroom
Fire starting: redundancy is king. fire striker, lighter, matches, etc. don't forget to bring your own kindling and wood if the park doesn't allow gathering
Games: young kids may get bored just hanging around the campfire, so plan to go on walks at night, or having fishing poles, or any other number of ways to keep their minds occupied.
Lighting: Get a good quality lantern - colemans are extremely good. Also, have a good flashlight for you, and decent ones for the kids. You'll definitely want a headlamp - you can some for $5 each at walmart and they are very handy.