Jesus’ brothers and sisters would surely have reminded him that since he was Mary’s actual son, when Joseph her husband died, he had a duty to take his mother into his own house and assume his responsibility as a son.
Jesus then took his disciples from the shores of the Sea of Galilee and went with them to visit his home town. He went into the synagogue in Nazareth to teach. The people there said “What’s this wisdom that has been given him, that he even does miracles! Isn’t this the carpenter? Isn’t this Mary’s son and the brother of James, Joseph, Judas and Simon? Aren’t his sisters here with us? And they took offence at him. Jesus said to them, “Only in his home town, among his relatives and in his own house is a prophet without honour.”” (Mark 6:1-4) The people who knew Jesus as he grew up and knew his family kick him out of the synagogue, jeering at him.
Jesus obviously did not stay in Nazareth, but went back to Capernaum. A short time after this Jesus is paying temple tax as a resident of Capernaum. He and Simon-Peter had so little money they had nothing with which to pay the tax until Jesus got a fish to cough up a four-drachma coin to pay the tax for both their households (Matthew 17:24-26).
My guess is that Mary officially became resident at Jesus’ house in Capernaum at this point. As a woman she would have little choice in this. But she may well have spent her time going round visiting relatives and staying with them for many months as women do in traditional cultures. Mary always appears in the company of Jesus’ brothers and sisters.
“After this he went down to Capernaum with his mother and brothers and his disciples. There they stayed for a few days. When it was almost time for the Jewish Passover, Jesus went up to Jerusalem.” (John 2:12)