Remind him she did FINE with him there as soon as you were. She probably had stage fright / didn't want to disappoint him (love the mind of a child, better to throw a screaming fit, than to miss one tiny aspect no one would care about!).
In my humble experience, the way to get over that is to have dad do MORE, not less. Times where you are both there together, and times when he's there alone. Which will also help her stage fright in front of strangers, as well as dad.
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Mmmmmm....
So in this Olympic season... I used to be in training for the Olympics. But my first several competitions I was a stilted, jerky mess. Absolutely shaking with nerves. My coach solved that by starting to invite people I knew beforehand. Not to make me comfortable. To make me MORE uncomfortable. I barely made it through my first routine.
Okay! Again!
Wha?
Okay! Again!
Okay! Again!
By the end of it... I was spot on. I don't even know how many times I redid my routine.
And then he took me to a bleeding different gym, and made everyone watch me. And again. And again.
By the time my next comp rolled around, I was pure authority. I was in my element. I OWNED that floor.
But it took Dozens and Dozens of stilted, jerky, failed attempts.