In the case of a divorce, do both parents have rights under FERPA?

Generally, yes.  Unless a school is provided with evidence that there is a court order, state law, or other legally binding document relating to such matters as divorce, separation, or custody that specifically provides to the contrary, FERPA gives custodial and noncustodial parents alike certain rights with respect to their children’s education records. A school may ask for legal certification denoting parenthood, such as a birth certificate or court order, from the parent requesting access.

Source: 34 CFR § 99.4