Nugent was a child actor, first appearing on screen at age seven in Secret Command (1944). She played small parts in four more movies over the next three years and in one of these, she and her sister Judy portrayed the same character at different ages. She was in a few popular hits, including Cheaper by the Dozen (1950) and Belles on Their Toes (1952) but as a child actor never quite made the transition from bit player to larger roles. However, as a teen Nugent grew into ingenue parts on television and in B-films. She was a supporting Actress throughout her career, which tapered off sharply after she married and had children.

In 1959, Nugent married actor Nick Adams after they dated for a short time. She appeared in a guest role for his television series The Rebel that year. They had two children together, Allyson Lee Adams (born 1960) and Jeb Stuart Adams (born April 1961).

In a 1961 interview Nick said, "Carol is my good-luck charm. My first real success, the turn of the tide, came right after I fell in love with her. Then I formed my own production company and we sold The Rebel." However, in the same interview Nugent said, "Let's not overdo the sweetness and light. Naturally, Nick and I had our problems at the start". Gossip columnist Rona Barrett later wrote that Nugent "was one of the most refreshing wives in the entire community."

In 1965, seemingly without warning, during a promotional television appearance on The Les Crane Show, Adams announced he was leaving her. This began a very public period of bitter separations and temporary reconciliations which lasted until his death in 1968. Nugent filed for divorce and custody of the children went back and forth between her and Adams but she was listed as his spouse on the death certificate and when he died she was living with their two children only a few blocks from his house in Beverly Hills.

In 2002 Nugent renewed her acquaintance with John G. Stephens who had been production manager on the 1960s television series My Three Sons. Her father Carl had been property master for the show. Stephens' wife, Actress Joan Vohs (1927–2001), had recently died from heart failure. Stephens and Nugent married later that year.