There is a serious problem with the school's identification procedures. Your daughter scored at the 99th percentile on the nonverbal battery. That should be the end of the story.
That said, it is also odd that the school is giving a second test that essentially does the same thing as the CogAT nonverbal battery. I suspect that they are doing this for political reasons and not because doing so better identifies students for their program.
Here is an interesting article by David Lohman, one of the developers of the CogAT that talks about how the more balanced structure of the CogAT is helpful for gifted identification:
https://drive.google.com/file/d/1vTZ2x-rMUBIPm3tlgYXhuyS5Beu5wQan/view
