Taking the OP's account of the event and the fact the batter was called out I think we can all make a pretty informed decision.
Not really. Were you there? Did you see exactly what happened? Did you hear the other half of the story? The other coach was arguing....and he was there. This type of play is a judgement call by the umpire, and since we were not there we cannot make an informed decision. We can make a "best guess" decision but not an informed decision. We only have a little more than half of the information. I "believed" the umpire in my prior post.
Do you have a reason to doubt her or question her integrity? There are multiple viewpoints, she gave you hers, and unless you are saying she is lying when she gave you the umpires ruling, is easy to say based off the ruling.
If you do not have the ball you cannot obstruct the runner, if you have the ball you can attempt to make the play. She stated her intention was not to hurt the girl and and had given no indication otherwise.
Coaches ands parents would argue the world was flat if it benefited them. Don't doubt yourself based on other people. But that being said, doing an occasional self checkup never hurts.