The answers to the two parts of this question are at least somewhat different. While the war and the Early Republic period were very close in time, they were also very different from one another. Throughout our history, wars have brought about situations in which women play roles that they have not played in times of peace. The American Revolution was no different.
During the American Revolution, women played at least some unaccustomed roles. Perhaps most importantly, women had to fill in for men who went to war. This meant that women took more of a role in doing things like farming and working as artisans. Some women played more direct roles in the war. Many women went with their husbands to war, doing things like cooking, cleaning, and nursing in camp. A few women participated in battles, though this was, of course, not at all common.
Once the Revolution was over, women’s roles returned to “normal.” The Early Republic period is said to be one in which women were expected to practice “republican motherhood.” This was the idea that the main role of women was to raise children who could participate in the life of the new country. Women were expected to educate their children well and to teach them good “republican” values. This meant that women had a role that was still centered around home and children, but it was at least a role that was given some degree of significance and dignity in the eyes of society.