Nina Eileen Watkins was born on May 18, 1931 to Arthur Vivian Watkins and Andrea (Rich) Watkins in Orem, Utah. Nina was the youngest of seven children. When she was a teenager, the family moved to Arlington, Virginia when her father, Senator Arthur V. Watkins, was elected United States senator for Utah. Nina met William Martin Palmer while studying at George Washington University. They were later married in Salt Lake City, Utah. Together they settled in Salt Lake City and had four children.

Palmer was very involved with many different organizations. She was an original member of the Utah Federation for Drug Free Youth, was a member of the Governor's Task Force on Youth Alcohol and Drug Use, and the Governor's Council on Volunteerism. Palmer started the Utah Association of Women in 1977. The Utah Association of Women changed its name in 1997 and became the Worldwide Organization for Women. Palmer worked to get her women's organization granted consultative status by the Economic and Social Council of the United Nations. She traveled the world to participate in United Nations meetings and conferences. In 2000, she was also elected to the Board of Directors of the World Movement of Mothers. Palmer died in Erda, Utah, September 6, 2021.