Thanks for reviving this thread, Teacher!
We've been doing a lot of biking this summer and have started needing to make repairs on the fly. The theory of my emergency kit has started to be enhanced with real life experience.

So far, the worst has been a broken chain on one of the kiddo bikes, a flat tire on mine, and some adjustments to the Kiddie Trailer.
I have a small basic emergency repair kit attached to my bike seat, along with a Leatherman Wave, and have been carry other stuff in a secondary pack. (i.e. a bright LED headlamp and removable front and rear LED lights, water bottle, etc.) I use a backpack to carry my extra gear and get home stuff when I'm commuting to and from work, and agree that a bike rack or panniers would be better. I also have a bag that's designed to hang from the handle bars, but it's too bulky when I load it, and it hangs in the front fender, obscuring the front reflector. So, I've moved that bag to my newest upgrade.......
We bought a bike trailer a month or so ago! It cost a whopping $25 at a garage sale. WOOHOO! It's designed to carry two kids and some gear or groceries, and it's awesome! I've towed two kids all over town with picnic stuff in the back, and we've also a couple of big road trips with my daughter in one seat, my backpack in the other, and picnic and fishing gear in the back cargo area.

The blaze orange flag is a little dorky but we'll probably upgrade it with a pink and purple streamers soon enough. LOL!