If you want disc brakes, the hub has to have a mount for the disc and the frame & fork have to have mounting points for the calipers.

But rim brakes -- whether they're caliper, cantilever, or V brakes -- are very effective at stopping bikes. They're still standard equipment on many high-end bikes. If you've got decent rims and pads and they're dialed in, stopping distance and effort should be comparable to disc brakes. Without knowing the specifics of your kids' bikes, I'd strongly suspect your braking problems have more to do with the quality and condition of the parts than the type of braking mechanism.

The "pedal backward" brakes you remember are coaster brakes, by the way.