Welcome, I hate flats just as much as everyone so on my Xtracycle where I could care less about saving weight I am running Big Apple tires (which I love) with Mr Tuffy tire liners, no flats yet and we have a good deal of goat heads and broken glass here.

With that being said once I take off my winter tires (just old mtb tires) I plan on putting some of the very thick "thorn resistant" tubes as well filled with flat attack tire sealant. I am sure this combo will make my mountain bike feel like a carbon wonder bike when I switch back.

As to dealing with changing flats with a toddler, luckily I have not had to deal with that yet but I use a trailer so I can keep him strapped in there and just hand him a few toys to play with. I would rather see someone strap their kid to a tree than let them run around un-supervised where there might be cars or people flying by on bicycles.

For the lock thing, most of the big guys (on guard, kryptonite, abus) make decent U-locks, just try to avoid the ones with a circular key, most of them can be picked into with a bic pen (search youtube if currious)