Will my family need to do visa runs if my husband gets a 1-year extension on his Non-Immigrant B visa?

Once your husband gets his yearly extension you take documentation from his company stating it's okay for you and your child to "piggy back" onto his. You show marriage certificates, birth certificates, documents from his company etc and the immigration office will give you and your child a matching extension.

Once you have those all you do are 90 day reporting at the immigration office. You will not have to visa run or border bounce.