“At will” and “right to work” are two different laws. You accurately described “at will employment.” “Right to work” laws make it illegal for unions to mandate the dues that you would pay them. It effectively defunding and disempowering unions.

According to Wikipedia, “In the context of labor law in the United States, the term right-to-work laws refers to state laws that prohibit union security agreements between employers and labor unions. Such agreements can be incorporated into union contracts to require employees who are not union members to contribute to the costs of union representation.”