That being said the batter should have been out. She was way out if the running lane when she made the bunt. Maybe the other coach didn't say anything because of the out at home.
Sorry no. That isn't how the running lane works. If you want to think about it, a right hand batter laying a bunt down is pretty much going to have to take the exact line to first base this girl did. and in this case, she did the right thing - passed by the fielder and didn't interfere with her the chance to field the ball and there was no play on her the fielder could have made. Absolutely not going to be an out. If the fielder fields it and throws to first and the runner now gets nailed in the back on a throw to first and she is in fair territory, it is a different call, but that didn't happen.
Ouch on the call at home. I understand how it happens - and when you consider he is looking down on the play as he is so much closer to it, I can imagine in his mind he may have thought he saw it, but yeah.