Going with the car, I tend to have similar to OP (although I have a can of "reinflate" stuff (which I know ruins the tyre but gets you home) rather than a pressure yoke for the tyre, and we have a proper spare tyre also.
My normal car kit has a pair of work gloves, Swiss Army knife, work torch, handwarmers (reusable), clean cloth as a rag, few cable ties, couple of mini bags of jellies and small bottles of water, mini 1st aid kit. Lives in the car all the time.
My self-catering box has increased over time and with things bought while away SC'ing! Small sharp knife, peeler, corkscrew, tin opener, wooden spoon (just 1), mini chopping board, handful of clippers, handful of pegs, string, matches/cigarette lighter (no smokers), 3 tealights, 100ml squeeze bottle of wash up liquid (usually enough for 4-5 days), 2/3 each of dishwasher tabs and laundry capsules, 2 bin liners, 2 j cloths, wash up brush and a scrubby sponge. And pack of cards.
And I have a relatively decent 1st aid kit from going on Cub Scout hikes that I throw in a bag as well. Along with a couple of microfibres towels as we do a lot of swimming/surfing.
I also throw in a couple of board games, couple of books and some paper/colouring pencils to allow quiet time and expressive time if needed.