At the point where electrical hook up/mini gennys/converters etc come into play...that just isn't camping any more. Sorry, I'm more of a wild camper than a South of France camper
Something to keep your beers cool? You don't need to shell out for a mini gas fridge or a 12v converter/cooler. A bucket and a nearby stream will be your friend. Fill it up and pop your beers (or milk) in. Obviously for extended cooling, keep the bucket in a shaded spot.
For cooking, I'd suggest the basics and a classic Bleuet Micro is all you need (along with a few pans and mugs etc.) and a box of matches.
Having said that one of my fave novelty* camping burners/stoves is the BioLite as it does have the ability to charge a device for as long as you keep the fire going (more of a boost than a full charge but good for a bit extra juice) thanks to a USB which is used via the converted biomass. Because it has an integrated fan too, it means it's able to both air dry and burn kindling almost simultaneously, even if collected when wet! The BioLite is a handy (if still pricey) stove with cool features but I am a fan of building my own campfire and the rewards it brings (even if just for the primal satisfaction). BioLite is probably seen as a hipster in the camping stove world and you could just take a couple of power banks if you really want some backup device charge.
I'd say wherever you're going camping though, keep it as simple as you can. A much better experience and applies to everything from the campsite to the kit. Kick your shoes off, reconnect with the earth and you and your kids "might" even learn a few basic survival/backcountry skills along the way! Oh and it goes without saying but leave your camping spot as you found it
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The reason a lot of you get "cold" tends to be more due to air mattresses! The further away from the ground the more air that will cool between yourself and your back especially with air that is "locked" into an air mattress. You genuinely only need to be a couple of inches above ground level and whilst the ground does/can get chilly, a half decent Thermarest pad and/or a couple of camping matts is the way to go; any in the NeoAir range will be fine. A semi decent sleeping bag also but no need for overkill on the tog number (not in summer and not whilst in a tent too), because the Thermarest and camping matts will be doing most of the work in retaining insulation/keeping the ground temp out.
Also vent your tent. Just leave your main inner "mozzy mesh" zipped right up but your outer should be left open a little. More modern tents do tend to have plenty of venting options integrated. Don't be tempted to camp in the lowest part of a site too. Two reasons, if it rains a lot...you'll be where the water runs to. But also, cool air generally drops to the lowest areas so make sure you're pitched somewhere a bit above the lowest ground. If you do get chilly - good to remember "top and bottom"...yep, whack on a hat and another pair of socks
*I say "novelty" because some elements of it are gimmicky although fun. It's probably more of a stove that is better showcased rather than overly useable in practice. The actual main burning function/s is/are pretty cool and the possibility of near perpetuity in regards fuel (it'll burn any combustible material) are a major plus. If not worrying about space/weight in your pack then worth giving a go!
Btw, the only part of this googled was the name of the camping stove (BioLite). I've literally thousands of hours of camping experience (wild and generic campsite). Also Mwooly on here will probably be able to offer some handy advice too.