HDFC coops have even another layer of qualifications and requirements than ordinary coops. Although HDFC coops are still private corporations like regular coops they have certain income restrictions and guidelines that they must adhere to in order to maintain their "HDFC" status and remain "affordable" and continue to receive tax subsidies from NYC under an affordable housing program.
I would be surprised if an HDFC coop board did not wield the power to approve or reject a purchaser particularly since the buyer has to be qualified under HDFC regulations. Right of first refusal limits the boards power to reject a sale with out having to purchase the unit.
Board approval means they can reject an applicant for any or no reason as long as they do not violate fair housing laws. You should consult with a lawyer experienced in HDFC coop sales.
The right of first refusal is a term used for condos, not co-ops. Co-ops require an extensive application, also known as a board package. They can then accept or reject the applicant. So regarding whether the co-op can force you to sell to them instead of your family member, highly unlikely. I would suggest you read through your offering plan and subsequent ammendments, or consult the managing agent on sales procedures.
Halstead Property, LLC