If it was just a personal arrangement between three people, why do you suppose it was recorded in the Gospel? (See John 20:31)
John was the "disciple whom Jesus loved," and the Greek says that he took Mary "eis ta idia" = "To his own" people, place, etc.
As I say, it's not just a personal arrangement, but symbolizes something much bigger. It's not for nothing that John's Gospel begins with the wedding feast of Cana (Mary: "Do whatever he tells you") and ends with John taking Mary "eis ta idia".
Good point!
Jesus answered, “The work of God is this: to believe in the one he has sent.â€
idia has the meaning of "uniquely one's own, peculiar to the individual". This adjective means private, personal. HELPS Word-studies
The Greek of the pronouns is in the genitive and is singular in both references.
This is, as you say, a personal arrangement between Jesus, John and Mary. It is between no one else.
As I say, it's not just a personal arrangement, but symbolizes something much bigger. It's not for nothing that John's Gospel begins with the wedding feast of Cana (Mary: "Do whatever he tells you") and ends with John taking Mary "eis ta idia".
The Bible I have records John opening with, "In the beginning was the Word...." and it concludes with his explaining if everything about Jesus were written the world could not contain the books.
It begins with Jesus and ends with Jesus. John is not about Mary much to the chagrin of the catholic. It is about Christ.
And recall, His last words on the cross were, "It is finished."