Which festival?
I find those thin, cheap fleece blankets (Ikea, Primark etc) a godsend on cold nights in conjunction with a sleeping bag. Even summer nights can get very cold if there's no cloud cover. I use them inside and on top of my sleeping bag plus gloves, knitted hat and bedsocks! The extra layers trap the heat and they're very light to carry (mine go in a big blue Ikea bag along with other sundries).
I see you're sorted with duvet and blow up mattress 
The walk from the carpark to campsite is definitely a drawback at bigger festivals. A sturdy trolley with big wheels is the way forward particularly if it's muddy. Even a small amount of rain creates ridiculous mud if it rest of the weekend doesn't remain dry. Try and time your arrival/unloading/pitching tent for a window of good weather (keep an eye on the hourly forecast). If possible arrive early for a good pitch/before impending rain! The car park is usually on grass and it will quickly get churned up ditto the walkways to and around the campsite if rain happens. You can be smugly in your tent by then having a brew!
I'm usually working so I have stuff like a tiny torch (99p ebay - came with lithium batteries, replacements available from Poundland) clipped to my lanyard or waist bag, antibac gel, metal water bottle on a caribiner. Poundland is quite handy for small bits and pieces like that for the kids. Those flat drinks pouches with a caribiner are useful and take up no room when empty. Check whether the festival allows you to take your own drinks into the arena. Water points are freely available, I use the small squirty squash things (Robinsons? Aldi sell a bargain copy at the tills) to perk up the often over chlorinated festival water.
Poundland/B&M also great for glowsticks, battery powered lights and solar tent lights.
Clashfinder (website) is handy if it's a bigger festival. You can print off loads of copies of the line up timings (and laminate if you're me ) to save money on ££ programmes. Kids can highlight their own. A3 works better for a tent copy as the type is really small! The line up only gets confirmed fairly close to the festival date.
Will the kids have phones? Smartphones are great for festival apps but they'll eat data and battery and regularly get lost/stolen. Cheap "festival mobiles" are probably the way forward for teens if you separate.
Earplugs are very handy (essential?) in the campsites at night.
I've never really done the whole cooking thing as we get a limited amount of catered food. I top up with snacks - crisps, cereal bars, Belvita biscuits, pot noodles, cupasoup, latte sachets, fruit, biscuits, sweets, porridge pots There's often an overpriced supermarket on the festival site or a shuttle bus to a nearby town/out of town superstore if you need to pick up supplies. I seem to recall it's not easy to leave the public car park once the festival is in full swing. That or you lose your parking space and may find yourself directed to a really distant car park on your return! It's handy to keep extra non-perishable food and drink in the car for later on in the festival week.