This one has really been clawing at me.
I feel so badly for your daughter that her mother is willing to do anything, including invading your daughter's privacy, her most personal thoughts, to win custody.
Were it me, I would try to use the mother's actions to show that she has no more concern for her daughter's well-being than this, that she thinks it's more important to use her daughter in this manner than it is to respect that she needs a part of herself kept to herself.
Speaking as a woman who used to be a teenage girl, this girl now has no place safe to go to unload, if you will.
This poor girl is going to have major trust issues and I hope she's in therapy now. Your stbx is destroying your daughter and any faith she might have in the oputside world.
Also, I'm not to sure about the motives of the GAL if they are taking this diary and reading it. I would be aghast that a supposed loving parent would do this to a child and wouldn't accept it from the "mother". Isn't the GAL supposed to looking out for what's best for the child? Does that include a parent who is willing to read her daughter's journal to gain a victory?