Christ declared their new relationship from the throne of the Cross.
But - according to you - He didn't mean anything important by it. If I understand you correctly; it was just one of those virtual things that Jesus did.
But we know what happened next. 'From that hour the disciple took her into his own household'.
This would have been a very odd thing to do if Mary had other children.
Not really. At this point none of His brothers and sisters were believers.
Jesus placed Mary in the care of John, the disciple whom He loved.
The Greek behind this indicates that John was to take her into his family. There is no special conferment of Mary being the "mother of the disciples" nor was Jesus giving Mary to all of us to be our "spiritual mother".
The family -His Mother and siblings- came to try and stop Him from openly preaching the things He was teaching, that were being twisted by the devout Pharisees and Sadducees, alarming the Roman occupiers. When the Romans turned Jesus over to the Sanhedrin to be tried as a criminal, this would taint the family and this in turn would cause the siblings to do much as Peter did, deny The Lord as their brother. Mary the Mother of Jesus came to the execution but it is not likely that her other children would risk that in that time, given the rustling of tensions between Rome and the Jews in Palestine.
By assigning John to be the son of Mary and Mary to live in his home thereafter was a sort of rebuke to the unbelieving siblings. It was only later that the brothers of Jesus believed and were born from above. James even presided over the first great Ekklesia council as portrayed in Acts 15.
Oh?
Joseph (OT) had some relatives that were not too trustworthy.
"A prophet is not without honor except in his own town, among his relatives and in his own home."