Final answer:
The dental priority category for family members of active duty members of the uniformed services is the TRICARE Dental Program.
Step-by-step explanation:
The dental priority category that identifies family members of active duty members of the uniformed services is known as TRICARE Dental Program. This program provides dental benefits to family members of active duty service members, National Guard and Reserve members, and retired uniformed service members and their families. It offers a range of dental services, including preventive, diagnostic, basic restorative, and orthodontic care.