It seems to me the best way forward would be to prepare the youngster for the Initial exam, as the OP states she is coping with the level of pieces. This will show the mother that you are not against exams. Definitely agree with explaining and showing the level required for grade 1. Also a discussion that each grade requires more at each level, not at an exponential rate, but it is not just a little extra difficulty.
Handled correctly, this mother could be an asset. She is keen, supportive and probably just very keen for her daughter to succeed. If she has not gone down the instrumental exam route herself, then she needs help understanding what is involved.
Agree with the advice above, do not make promises. Explain the work involved, acknowledge that the foundations are being laid already at home, but stress it is not an easy or guaranteed route. Also stress, the daughter has to want to do it herself, and to keep practise time fun, or there will be blood!
Oh, I'm definitely not against exams, just prefer not to be told when they're going to be
As to the daughter wanting to do it herself, I totally agree and I'm not 100% sure that that is where we are at the moment. Time will tell, I think.