Catcher hits bat with throwback

[TriggerMN]

Runner on 2nd. After a pitch, the catcher's throwback to the pitcher hits the bat, sitting on batter's shoulder, and the ball scoots away. Runner advances to 3rd. My partners said kill it and send the runner back to 2nd. I said play on. Who's right?

Is it a judgement call? What if the batter hits the ball on purpose to move a runner up? Are you calling either the batter or runner out for interference?