i thought mentioning our religion might be counterproductive.
I don't think so. It may not be a major point (most children, after all, attend co-ed schools, whatever their religion), but it's probably worth a brief mention if supported by a religious leader.
she has really matured in her outlook and in respect of her commitment to her school work.
That approach sounds better, and I would now suggest including a couple of lines in your written case:
"Since she started year 6 she has become more sensitive, and her perception of boys has changed. She is finding them disruptive and immature! She has really matured in her outlook and in respect of her commitment to her school work, and she particularly wants to attend an all-girls' school where she feels she will be able to flourish and focus on her work."
"We also have religious reasons - please see attached letter of support."
As I've written elsewhere, a lot will depend on factors outside your control:
• How strong a case the admission authority puts forward to resist further admissions.
• (Probably) how strong a case the other appellants have.
• How strict the appeal panel is in exercising its judgement.