The stain should penetrate 1/32" or more, so unless the kids are going to work on the floor with a chisel, I doubt minor scratches will be any more noticeable than the same scratches on an unstained floor.

It depends on the wood, though. Oak shows fewer problems than maple, for example.

A quick wipe with Old English and the scratches disappear. We just had ours refinished in Feb and got quite a few scratches during remodel. GC suggested Old English and it has worked. We have medium brown I'd say. I have not seen scratches from our dogs and kids, (yet) only from moving furnitures and appliances.

We have some light scratches in our newly refinished medium brown floor, but unless you're looking for them, you really don't see them. I'm going to try the Old English suggestion to make them disappear.