I think the premises of this is false.
The rate of women in the workforce went UP in the 1950s, typically seen as the peak of women not working. Women have been in the workforce in high numbers since the beginnings of the industrial revolution in the US. Women were not demanding to join the workforce, and in fact, the concept of not working and homemaking was seen as an economic luxury. What actually happened were that a subset of women who were highly educated and economically comfortable demanded more equality in the professions, which were entirely male dominated. The development of suburbs and mass advertisement meant that homemaking became an available and intricate lifestyle for more women, who just so happened to be generally more educated and with more valuable work skills than the women who were working at increasing rates. The narrative that men would not let women work is so laughably false that it is ridiculous that this notion still exists; men were fine with women working, provided they did low wage and menial work and did not threaten male control over the professions.
As for children, they too were in the workforce. In fact, this was seen as a significant social ill, and laws were made to prevent this. But children did still work (albeit in more regulated functions) after child labor laws were passed, and today, a 14 year old is legally allowed to work in most states in the US. This kind of pro-child labor movement would be dismissed as either astroturfed by Chamber of Commerce types who liked paying low wages, or it would come about in the midst of a national economic emergency, where children felt a need to pick up the slack for their families, in which case unemployed men would obviously oppose such a movement because it would threaten them.