As well as water - what about some cans of drinks (like cola, lemonade etc - whatever your family likes) and some dilutable drinks (like orange squash). Apart from being able to drink cold drinks with the squashes, I sometimes in the depths of winter make them up using hot water for something really comforting.
Matches, candles, firelighters/kindling, fuel for whatever backup cooking you have (a bottle of gas, a bag of charcoal, can of kerosene), extra container of gas for the car/truck, batteries for torches/radio (maybe even one of the windup torches/radio/mobile phone charger).
And apart from prescriptions, having a well stocked first aid kit might be useful - things like bandages (both band aids and larger ones for sprains), cleaning fluids (alcohol?), cream for cuts and burns, painkillers, deep heat spray (for muscle strains etc). (I may have gotten some of the ways you describe them wrong, but I amn trying to think of the kinds of injuries you may get - slips on ice, strains from digging/cutting wood, cuts from working in poor light). Maybe a couple of heat pouches (they heat up when you mix 2 parts) and a "space blanket" in case someone gets very chilled.
Lots of distractions that don't need power - so paper and pencils/paint, packs of cards, board games, books, puzzles. Not that you need to buy more necessarily, just make sure you know where to find them easily. But a new one produced at the right time may also be a useful standby.