I think you are in for a TON of fun!
First off, I would get the BIGGEST tent possible. When you need to corral the kids, it will come in handy for sure. It sounds like you will get plenty of opportunity to use it too. Amazon has an amazing selection of tents in all sizes and price ranges. It sounds like with 7 people you seriously need a hefty size.
Big tents:
http://www.amazon.com/mn/search/?_encoding=UTF8&camp=1789&creative=390957&field-keywords=family%20tent&linkCode=ur2&tag=motorhomeandrvstore-20&url=search-alias%3Daps&linkId=DBV3LG6344XGZUAN
I would also consider adding a 2nd enclosure such as screened tent or screened room or portable gazebo this is a way to corral the younger kids by day, while still giving them great views of the outdoors.
Coleman makes an awesome 8 sided one.
http://www.amazon.com/gp/product/B00339C3FA/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=B00339C3FA&linkCode=as2&tag=motorhomeandrvstore-20&linkId=32H2SZSAPIXUAERU
I worked in tourism for decades. I met a fascinating family that loved to travel. They bought each child and adult a backpack that fit them. Into the little backpack went their clothes and toys for the trip and that was IT. Even the couple packed in a backpack each. They camped, they flew, they sailed, they went by car, but they stuck to their 1 backpack per person routine.
They said it enabled them to travel far and wide without worrying about lost luggage, too much luggage or bell hop tips. The kids learned to play with what was around them (nature, playgrounds etc) they learned if they trashed their clothes and ran out, they had to live in the dirty ones anyhow or go wash them (if available). They said it enabled them to make quick get away trips too, the kids (as they grew older) could pack their own backpacks in just a few minutes.
Next, I would get an aluminum hitch mounted cargo carrier. Aluminum carriers are much lighter than steel ones. Get one heavy rated, like for 500 pounds.
http://www.amazon.com/s/?_encoding=UTF8&camp=1789&creative=390957&field-keywords=aluminum%20cargo%20carrier&linkCode=ur2&tag=motorhomeandrvstore-20&url=search-alias%3Daps&linkId=IHKR2B2UQJBFMON5
On top of that you can add a big storage box or just strap down the tent, cooler and other stuff. I imagine you will want the biggest cooler possible, which will also double as a bench at the campsite.
Install a hasp and lock and the cooler. Otherwise crafty raccoons will help themselves when you least expect it.
Get a vinyl table cloth in excess of 8 feet so you can cover the entire picnic table with one cloth. Some camps have 6 feet, others have 8 feet. I travel with a 108 inch table cloth and never regretted it because it fits all picnic tables.
Make sure everyone has their own battery light. You can get assorted ones at Dollar Tree for just a $1 each. You can also get lanyards so they can wear them around their necks. (I do this too!) That way they each have a light to find the restroom after sunset or anything else they need after dark. Too many families show up with too few lights. Best to have one for each person as a minimum.
Enjoy!