What is two ways that the new deal expanded and limited opportunities for women?

One way is that they began working in government institutions and the number of employed women rose drastically compared to how it was before. There was also a high amount of women who held important government positions which showed that the jobs were not just bad ones that were poorly paid and with no prospect of future success.

A way that it limited them was that there was a lot of misogyny. Women in the workplace were paid less then their male coworkers even when they worked at the same position, and they also faced harassment from their colleagues, most often in the form of sexual harassment. Many misogynist employers wouldn't even give them jobs because they perceived male workers as better.