A couple of strikes on the inside of the plate might help the batter change his stance a bit. Nothing worse than getting beaned on the elbow only to have a strike called (of course, you do need a competent umpire to make this call).
As for the double steal in particular, you mention that was "on my son" - did your son make any attempt to throw either runner out? If an attempt was made, it would have either been behind the batter (which having a right handed batter move towards the plate would benefit) or would be in front of the batter which should have resulted in contact on the plate itself. Was it just that the catcher made no attempt and therefore no interference?
You also mentioned stepping on the plate during a swing - my understanding is that this is an out (if during the pitch - not immediately after) and should have been recognized and called. Not sure how this kid could be a very good hitter and end up stepping on the plate during a swing.
Again, the best way to deal with this is to throw strikes inside and have the catcher execute throws normally - even if that entails the catcher charging through a batter who ends up standing on the plate. I have heard some different interpretations of what space the batter "owns" (i.e. can they simply stand still within the batters box regardless of other action) but I have never heard of the batter having any rights to occupy the plate after the catcher receives the pitch.