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I did this for years, 1 to 2 week or just weekend excursions with my wife & daughter. You're going to find that every simple little thing can be an adventure for the kids. (and the "grownups"!)

Are you hoping that this becomes a family routine? Run off on every available weekend for some woods/down/family time?

I would first recommend that you do a family planning session with Mom and the kids. ( Cheat and discuss the overall plan with Mom first). IMHO, the more input the kids have, the more they feel like a real part of the whole thing rather than being dragged into something by Mom & Dad.

Gear in general, buy the best that you can afford. Good gear pays for itself in comfort, reliability, and performance. You're going to be putting this stuff through its paces, setting up, tearing down, living in it and piling it all, sometimes haphazardly into the vehicle.

Tents, You're going to be in a lot of different locales and weather conditions so I would definitely want something with a full fly. Drying out a tent when traveling is a distracting, time consuming, PITA. I would get two of them, one for the kids & one for the adults. A good 2 person should be big enough for them at their age. Understand that they will want to get away from the grownups sometimes and for them, having their OWN TENT is awesome!
Understand also that the kids will most likely end up sleeping in your tent most of the time so I would look for a good 4 person tent.

Sleeping bags, buy ones that are rated for the LOWEST temperatures you will encounter, It's very easy to partially unzip a bag that's too warm but more difficult to make a cold bag warmer. Avoid the real cheap ones, the insulation tends to bunch up in spots leaving you with a bag that has both lumps and cold spots.

Ground pads (padding directly under your sleeping bag), I would first try something like these, test them at home, along with all your equipment, and if they're not adequate you can upgrade to something better. Any worthwhile outdoor store should have a variety of sleeping pads already out & inflated for customers to try out. GOOD SLEEP is everything.

FOOD is also everything! for car camping cooking in a group I would find a Coleman Gas stove. I've had one for decades, they just WORK!
Also, you can run it on the unleaded gas in your gas tank, just buy a 6-8 ft piece of CLEAR 1/4" ID siphon hose and you've got as much stove fuel as you have gas in your vehicle. I've been doing this with mine since the mid- 1960's.

Eating gear, I Still have a basket that holds all the plastic cups & dishes, utensils, spices, Aluminum foil, even a smallish (10") skillet & cook pot. It's real handy to have it all organized in one package when you're hungry, or anytime.

Camp lighting. HEADLAMPS FOR EVERYONE! IMHO, These are cheap & reliable, and easy to find & replace if necessary. (Buy many extra batteries...)
For the Camp, one of These provides a soft light around the picnic table in the evening. The candle itself is readily available and easily replaced.

Water is life, You won't shouldn't need a filter at a campground but everyone still should have a personal water bottle. Custom water bottles for kids and adults can be fun.

First aid, bug spray, and band aids are a must for both the kids & adults.


That's the basics, get out & hands on shop, compare, and enjoy the trip!

EDIT, I just saw Big Agnes tents on closeout at REI, IMHO this looks like a good deal for a 4 person car camping tent. It's a good time to be shopping for gear, lots of stuff on sale right now. Check out Backcountry.com and Sierra Trading Post for decent gear at decent prices. YMMV