Batter Interference - Runner steal third?

[mike miles]

Baserunner attempts to steal third.

Cathcer receives ball cleanly comes up to throw (note does not "hop step" in front of plate nor does the catcher "favor the lefty batters box, hitter is right handed) and the throw hits the batters bat then helmet.

It has been my "opinion" ( I know I should no the exact rule chapter and verse) that the batters box is safe haven for the batter providing he does not intentional try to "interfere" with the catcher and it is the catchers responsilbity to avoid the batter while throwing to a base when a batter is in the box.

So "if" the batter "intentionally" interfered I would have called the batter out and put the runner back on second.

If there was no interference the runner advances, its a ball to the batter and the ball is still live.

Was I, am I correct?

Can someone reference the exact rule please. Does this vary by type or league of play? This example was Little League - Juniors (13-14).

Regards,
mm