by the way, there are thousands of reasons why she may be having difficulties. i had a child very similar to what you describe last year. she was diagnosed with shortterm memory problems and i think language processing problems. she was very bright and sweet- just honestly could not retain the information.
if her parents refuse to give permission and it is clear that she needs help, wouldn't that be considered neglect on their part? and therefore be grounds for intervention by the county/state? I would collect as much documentation as possible from teachers, etc... i don't know who you should contact though. sorry. probably the state or county.
in Texas schools you cannot even enroll them in school without legal guardianship- I mean if they get thru the front door and the office finds out- they will be sent home the same day,,,,, so these sorts of problems don't become issues- she needs to be evaluated- Could her mother come to the school to ask for the evaluation- Sometimes schools refuse intervention til after kindergarten- sometimes 2nd grade- I don't agree with it but that's the way it is sometimes, although speech therapy would surely be offered this early.
Mother needs to try though-
It will be easier to get your granddaughter the support she needs if you have legal guardanship....You should be able to get an independent assesment from a specialist, but in terms of school system evaluation, you need some sort of permission letter from her parents....You may want to pursue legal guardanship - if her parents are not in the picture, you would end up doing that anyway
Good luck
Your school system should have some type of "testing" for children who are having difficulty in the classroom. I do not see how parents could not accept the efforts of the school system to better help your granddaughter. Any other thoughts ....