Not a very technical observation but an observation. 4 year old weighs between 35 to 50 pounds and stands about 3 1/2 -4 feet tall. In order to pick up the kid you have to hold it at least chest high in order to run.
Unless the pervert turns around to use the kid as a shield I see no problem shooting him in the calf, ankle area and dropping him.
I'm glad it all turned out well for the Family.
I have no issue with a shotgun for home defence, sometimes it can be the best choice.
When I deployed often I kept a 00 loaded 870 in the Master closet. 4 doors between the wife and Son (who slept in our bed at 2) and a rather large and angry doberman.
The instructions were keep the doors all locked and closed, if you hear a noise call the Cops take the phone and get in the closet.
Stay on the line and shove the barrel under the door knob, if the door knob turns before the Cops get there pull the trigger.
I often wodered what a door knob would do to a burglar when propelled by a shotgun blast.