Does this letter sound grammatically correct?

First of all, FAFSA is not a "loan". It is simply a form that the government uses to assess an applicant's financial status. Therefore the phrase "to her FASA [sic] loan" is incorrect.

Second, whether or not you THINK your child is independent, or whether or not you intend to contribute money to your child's education... your child is NOT "independent" unless your child is:
** 24 years of age or older by December 31 of the award year;
** an orphan (both parents deceased), ward of the court, in foster care or was a ward of the court when 13 years or older;
** a veteran of the Armed Forces of the United States or serving on active duty for other than training purposes;
** a graduate or professional student;
** a married individual;
** a custodial parent or guardian of legal dependents;
** an emancipated minor or in legal guardianship;
** a homeless youth; or
** a student for whom a financial aid administrator makes a documented determination of independence by reason of other unusual circumstances.

You see, you are expected to contribute to the cost of your child's education. The fact that you do not intend to contribute is not relevant.

Third, if your child DOES meet one of the conditions listed above to be considered an independent student, you are not required to complete the FAFSA, so no letter is necessary.

If you are simply refusing to provide your information, then say so. But do not say it is because your child is "independent". That is not your determination to make.

"My name is ABC. I am the parent of xxx. I refuse to share my personal information on my daughter's FAFSA form.

Thank you,
ABC"

Sounds great