Fair ball hit with hands

[DadO3]

I've searched the forum and I can't find a specific reference to this situation.

With runners on 2nd and 3rd.
My son, in an 11-13 year old league, swung at a pitch and the ball went between the 2nd and 1st baseman. He reached 1st base.

The runners on second and third scored.

Here's the gotch ya.
The ball actually hit his hand when he swung and not the bat, although he was holding the bat.
The call was made as a hit and the runners were not forced to return to their base since "the hands are part of the bat".

The other coach argued that this was a "hit by pitch" and therefore should have been a dead ball.

What should the proper decision be?

Thank you.