Batter's Box - Stay In or Step Out?

[mg43]

In our specific case, as soon as the pitch was received, the catcher threw into our batter's back. Our batter did not move from the box. I accused the opposing coach of instructing the catcher to throw into her back and he replied that I was correct. He went on to say that after the pitch previous to this one, our batter stepped back to get the signal from the 3rd base coach and was in the way of his catcher trying to make the throw. So, he told her to throw the ball toward 3rd and into our batter on the next pitch. He said he wanted the easy out for interference. He thought his catcher understood that she was not to throw if our batter was in the batter's box. And he offered no apology to our batter.

If the home plate umpire had concluded that our batter was not breaking any rule by standing in the box, what should the ruling be? Should she be awarded 1st base for taking a throw in the back? If so, what about the runner at 3rd.

In our case, our batter was told that on the previous pitch she was out of the box and probably should have been caleld for interference, so no call was made on the throw into her back.