A mother with small children on Rosh Hashana
If you can’t pray because you are occupied with caring for your children, then in principle the law says you are exempt from praying. But if you can find a little time to pray, that would be very worthwhile.
Women are exempt from hearing the shofar-blowing but nevertheless most are stringent and go to hear it. However, a woman shouldn’t be stringent if it means bringing her small children to the synagogue where they will disturb the congregation who want to properly hear the shofar-blowing. (Shulchan Aruch 589:3 and Yalkut Yosef ibid:5).In any event, many synagogues offer a special shofar-blowing for women in the late afternoon hours. If you want to be stringent and hear the shofar-blowing you can go to one of these places.