We have camped extensively with two boys now aged 8 & 9. (When I say extensively, over the last 6 years we have probably slept over 500 nights in our T6 Beach).
If the weather is dry *and* you are only camping for 1 or 2 nights, don’t bother with a driveaway awning. Get some side panels for the sun canopy instead. If you peg them out at an angle they can give you up to about 9 sq metres of covered area.
If staying for an extended period we use a Vango Hexaway driveaway awning. It is our indoor kitchen, living room, dining room and storage area. We love it, and I think it is really stylish.
You will also want a fridge. We have a Dometic CFX28 which is probably the smallest you can get away with for a family of four. We can stuff it with sufficient food for four for four nights, but no room for beers or wine until day 2.
We take with us a Campingaz 907 bottle, a double burner stove and a Cadac BBQ. (A 907 bottle lasts us about four weeks: hot drinks for breakfast, and one hot meal per day.)
For bedding you need sheets upstairs and downstairs, pillows, duvet for downstairs and sleeping bags or duvet for upstairs (we let the boys choose).
As you camp more you will be able to gauge how much you need and it is almost inevitable that there are things that you think you need but never use. For example we hauled a fly screen for 40,000 Km around Europe for a full year when the boys were 2 & 3 and never used it once.