I know you were specifically thinking about a survival bag for the girls, but I was thinking about a few things to mention to you from a female perspective. First off, do they all know auto basics 101 to help prevent this getting stuck scenario, such as checking the oil, changing a tire, adding coolant or water if overheating?
I ask this because I've recently been thinking about how I have amazing parents that have taught me a lot, but never told me to check the oil, or showed me how to change a tire, or jump a car battery, before putting the car keys in my hand. I don't think it's intentional, but girls just aren't taught the same things as boys. I was never told I wasn't capable of fixing shit and building shit, but I also wasn't told that I was capable- those things were never expected of me. I did dig a lot of trenches and I hoed a lot of weeds though. That's a great way to punish your kids for drinking btw, make them dig pipe and landscape hungover- either they'll quit drinkin', or your yard will start looking fantastic!
I attribute most of my familiarity with motors, appliances, and electronics, as well as camping and survival skills to TG, not that I have much, but enough to get out of some jams and enjoy camping regardless of the weather.
It's also good to familiarize them with the MacGyver strategy. Just because you don't have an item, doesn't mean you can't make it or make something else work. I've been slacking lately, but I usually try to wear a belt in case I need a tourniquet, to secure something, to tug on something, etc... I also keep a pocket knife on me at all times. The knife I carry is small and unassuming, but I could do some damage with it, cut a seat-belt loose, make kindling, use it with flint or magnesium rod as a fire starter, etc... A hank of rope is always a good idea. Of course Duct tape can be used for pretty much anything. I also keep a tool bag in my car with a coping saw, a hammer, pliers, wire cutters, etc... I keep a little photon key-chain light on my keys that is bright as shit, perfect for looking under the hood. Rain gear is nice but you can always throw in some emergency ponchos (maybe in the fanny packs) if your worried about the space and weight. A tarp might be a good idea, they can role up in it to stay warm and dry if they're hiding out for the night, and it's small enough to take up minimal space in a backpack. I don't know if it would be overkill for your particular situation, but they make compact solar chargers that can be used to charge a cell phone, they work pretty well, in daylight of course.
That's all I can think of for now...