When a marriage ended, the children stayed with and were legally part of their father’s family. So a woman who remarried generally would not raise her own biological children. When Pompey divorced his third wife Mucia Tertia, her children (then in their early teens) stayed with him. She herself remarried the brother of Pompey’s second wife, Aemeluis Scaurus and had children by him as well. Though now attached to a different family, we might wonder how much connection she still had to her children by Pompey.
Many remarriages seem to have happened only once the children of the previous union were at least in their early teens. When Julia Caesaris became Pompey’s fourth wife, his children by Mucia gained a stepmother very close to their own age. Marcia’s second husband had a daughter, Hortensia, old enough to already have been widowed, by the time she married him.
There were also, however, several cases of people raising quite young stepchildren. Marcia’s own father, Lucius Marcius Phillipus, only remarried to Atia Balba Casonia after Marcia herself had married Cato the Younger, though in this case he gained two young stepchildren: Octavia Minor and Gaius Octavius. Octavia herself wound up raising quite the large brood of children including her biological children by Marcellus and Antony and her stepchildren through Antony’s unions with Fulvia and Cleopatra VII.
Bradley, K. R. "Remarriage and the Structure of the Upper-Class Roman Family." In Marriage, Divorce, and Children in Ancient Rome, edited by Beryl Rawson, 79-98. Oxford: Oxford University Press, 1991.
Corbier, Mireille. "Divorce and Adoption as Roman Familial Strategies. In Marriage, Divorce, and Children in Ancient Rome, edited by Beryl Rawson, 47-78. Oxford: Oxford University Press, 1991.
Pomeroy, Sarah. Goddesses, Whores, Wives, and Slaves: Women in Classical Antiquity. New York: Pantheon Books, 1995.