The Household

"The loud voices of her two daughters greeted Aemilia as she reached the top of the stairs. The children's quarters was a large, spacious room with windows that looked out into the atrium on one side and the street on the other. The girls were sitting on the floor, rolling a beaten leather ball between them. Aemilia let herself pause for a moment and watch the two as they played. Claudia Minor had dark curls like Aemilia, while Claudia Major's hair was straight and a shade lighter. Marcus could be heard in the other room, giggling at some joke with his tutor. He had Aemilia's curly hair as well. 
"Clapping her hands, Aemilia caught the girls' attention. From behind her two servants brought in a loom and spindles, followed by a large amount of undyed wool. Immediately Claudia Major sat at the loom, waiting as her mother and younger sister began to spin thread."

Although Roman households are known for being run by the paterfamilias, or the father of the house, the wives had a hand as well.

The wife of the paterfamilias was known as the materfamilias (mother of the household), and though she may have been hidden behind the power of her husband, she was in charge of managing the household day-to-day. 
Even wealthy women were tied to household duties. Had likely been taught the ways of managing a household as a young girl, and now held those responsibilities. They still spun thread and wove cloth, but it was more a symbolic than utilitarian practice, one that gave them the image of an ideal Roman woman. In addition, she often served as the teacher of her own daughters - passing on the information she had learned when she was a girl.
However, that was not the end of her duties. Women of the household also oversaw the servants and their various tasks, such as cooking, cleaning, or making clothes. They also controlled and kept track of the money in the household, often doing the accounting themselves.

Roman Painting - Villa dei Misteri - Pompeii - Italia. Courtesy of commons.wikimedia.org.

SOURCES:

http://www.pbs.org/empires/romans/empire/family.html
http://www.pbs.org/empires/romans/empire/women.html
http://travelswithnancy.com/women-ancient-rome/law-&-identity.htm
https://www.ancient.eu/article/870/ancient-roman-family-life/
https://commons.wikimedia.org/wiki/File:Roman_fresco_Villa_dei_Misteri_Pompeii_004.jpg