She took courses at Rutgers Law School and became State Legislation Chairman of the New Jersey Federation of Business and Professional Women.

The bill criminalized "discrimination in the rate of wages on the basis of sex" and later became a model for federal legislation.

In 1970, she helped Representative Martha W. Griffiths to bring the Equal Rights Amendment to the floor of the House after it had stalled in committee decades earlier.

Dwyer described herself as a "progressive and moderate Republican", who supported civil rights legislation, women's rights, Social Security benefit increases, housing renewal, mass transportation, food stamps, medical care for the aged and anti-poverty programs, making her one of the most liberal Republicans in the House of Representatives.

[17] Dwyer was one of thirty-one Republicans in the House to vote in favor of the Comprehensive Child Development Act of 1971.