That she was crying when she erased her mom-approved answer to the question makes me think she didn't want you to know he had been coerced into writing something she knew you wouldn't like.
That's a lot of pressure to be under for a kid. At least with me, it was just me against my parents, I knew what they wanted to hear and I said it even if I didn't feel it, but nobody had to know. With you and your ex, she can't win.
As she gets a little older it will be easier for her, I think. She'll have to go to meetings when she's with her mom, but she'll still have you and will be able to get away for a little vacation from the cult sometimes. She also won't have the pressure of disappointing 2 parents when the time comes for her to make a decision about if she wants anything to do with JWs.
I think it's definitely a good thing she has you to keep her grounded. She will learn how to cope with all of it eventually.