In a Roman family, the father was called the paterfamilias, and he had complete power over his wife, children, and slaves for the rest of his life. If the father's father was still alive, he was the boss of the family. Fathers could even put their grown sons to death for serious crimes like treason.
Each house had a cult of ancestors and hearth gods, and the paterfamilias was its priest. People thought that the family had a "genius" (gens) that had been passed down through the generations. The gens was a link between the living and the dead family members.
Children who were really their father's belonged to his family. If the husband started the divorce, which didn't happen often, the father kept custody. The father could cut ties with a baby if it was born with a defect. This meant that there were not enough women in Rome.
The father of the bride had to give a big dowry to the family of the groom, which put the rest of the family in a bad financial situation. Also, when a father died without a will, his daughters got an equal share of his estate. This moved assets from their family of origin to their husband's family. No wonder women were called a burden on the economy.
At first, slaves were treated well because they were seen as part of the family. They could save money (called "peculium") and use it to buy their freedom. When slaves were freed, they became full Roman citizens and usually worked for the family as hired help or paid labour. Slaves weren't abused and treated like things until a long time later, on the huge plantations that wealthy Romans had built up.