It is good to start by simply convincing family to have a permanent first aid kit in their vehicles. (And one in the house!)
It strange that nobody ever think it is strange to have a bag for a baby with extra clothes and food and even medicine. You will have clean clothes in the vehicle for even yourself having a toddler.
Remember to take the basic bob with you if you quickly jump from your vehicle into someone else’s. I know of a very prepared guy who got stuck next to the road in winter … thinking about his bag in the boot of his own vehicle – that had the extra clothes, food ..