Dropped pitch, kicked by batter
 

Pitcher delivers a ball to the catcher who drops the ball and it rolls behind the batter. The catcher gets up to make a play on the ball trying to keep the runner at third from scoring. The batter backs up out of the box to allow his runner a chance to score. In the process, he kicks the ball with the back of his foot which knocks the ball way out of play. Seeing this, the 3rd base coach steals home.

My questions are: Is it interference? Does the intent of the batter play into the umpires decision either way or is it irrelevant? If it is interference, is the batter out? If it isn't, what's to keep a batter from "accidentally" stepping out of the play and either a) hitting the ball away from the catcher or b) stepping such that he puts himself between the catcher and the runner so the runner can try and score?

Thanks in advance for you help.

See if I follow this.
 

First paragraph is fine up until the last sentence. Did you mean runner, not coach.

Second paragraph, yes, yes, yes if he believes the batter acted with intent to hinder, confuse or impede. Response to a) all action is stopped and runner must return to base, and b) runner must return to base and batter is out.

The batter is not yet a runner. If I'm not mistaken, with less than two outs and the batter interfered on a play at the plate you call out the runner. With two outs, the batter is out. Not sure if this fits the op though. Sounds like R3 stole home because of the INT.

If the runner wasn't going originally and the batter accidentally kicks the ball, I'm killing it right then. Weak int.

Intentional kick?
 

Interference on batter, runner is out, not batter.