I have learned in my very short time as a gym parent that I am best at being a mom and letting the coaches do the coaching. When I know she's struggling, I bite my tongue. I don't ask about it but I do listen to her frustrations when she shares them. I tell her I'm proud of her for her hard work and tell her to just keep doing her best, it will "click" when she's ready. Then I change the subject.
These fears are mental and the more we talk about them the more they think about them. I can honestly say, the less time my husband and I spend in the gym or talking about gym, the faster she she is able to work through her fear. No audience, no pressure.