If you can do expedition planning, you can do camping planning.
You and the kid need to be clean, warm and fed. Pack for a cold tent and rain with a possibility of a brief lull in the deluge where you will be flashfried under the twenty minutes of sunshine. With wet socks, obviously. So full coverage stuff for legs and arms, a hat, socks, underwear, waterproof jacket, gloves, sunblock, sunglasses and bug repellent.
You need to sleep somewhere. So sleeping bag, something to use as a pillow (spare fleece blanket?), extra thing for warmth.
You're apparently bringing bikes. So a first aid kit - include a tick tool, wipes, dressings (better than normal plasters), paracetamol/calpol sachets - and he can deal with bike related shite.
Gaffer tape and binbags.
Personal hygiene stuff - sanitary stuff, wipes, nappies, barrier cream (useful for you as well), soap, flannels as substitutes for towels, toothbrush and toothpaste.
Food stuff - stove, kettle, mugs, a plate each, a fork and spoon each.
Add in the preferred cuddly item, a means of light, a map, a powerbank for the phone, spare tent pegs and the number for the nearest B&Bs so you can abandon him if you get there and find that he's forgotten the groundsheet and you're pretty much golden. Even if you have wet socks.