Kids here too, three of them.
My best suggestion for prep with kids...
...take them on camping trips, road trips, hiking trips, etc. I have found (inadvertently) that having spent the last 4 years taking my kids on dozens and dozens of trips and collecting the gear and knowledge to do so...was in fact...prepping. I've got a great BOV that I didn't even know was one until recently. Now that I have begun formally prepping, I am finding how valuable that experience has been. It has given me a good understanding of what minimal supplies are necessary, and it has given my kids an understanding for it as well. They are easily disconnected from the joys of modern society and are comfortable with simplicity. They have also learned various outdoor skills and continue to each trip.
If you are planning to leave the City with the SHTF. Then start practicing now. Leave the City at least once every month and go play in nature. Do it in all the seasons, so you have gear for all seasons and experience in all seasons. Even if you aren't up for camping in winter, take a minimally-packed road trip to hotel in some small mountain town and spend the day hiking. You'll love every minute of that prepping with those kids of yours.
We started camping and heavy mountain play when my kids were 2, 4, and 6. It was just for fun back then...still is now... However now I see the alternate value to it all more clearly. I also see kids that are more prepared for leaving home...and everything it contains.