During the crucifixion, why do you think the Lord established a relationship between his mother and John when his mother had other children in the house (James and Jude, etc.)?

This text is from a transcript of a talk by David Gooding, entitled ‘Four Journeys to Jerusalem’ (2009).

I confess I'm not well read up on our Lord's relatives, but maybe they weren't yet converted. But secondly, it was a question of John taking her into his own home. Thirdly, it could have been that John was more well off than some of the others. You will notice that John, when Christ caught him, left his father and 'the hired servants' in the boat (Mark 1:19–20). He and his father were employers and had employees working for them. They were in a bigger way of fishing than was Peter who manned his own boat. And it may be that John was more in a position to look after her. And finally, John was a young man, and he looked after her for years. She lived with him, according to tradition, in Ephesus, when he was there.

Also it seems to me it was no accident that our Lord said it at the cross because, first, Mary had come to the cross, and he was about to give up his spirit, and he wanted somebody to look after her when he was gone, so to speak. And it was the John who leaned on his bosom, who was so near the Lord—in the Lord's affections—who had the mother committed to him to look after.

Secondly, there is the meaning of 'the cross'. I don't know whether it is still said around here, but you know the way it is sometimes said, 'I've got very bad rheumatism, but that's the cross that God has given me.' Well, that's talking nonsense, actually. It has nothing to do with the cross. The cross is what the world gives you. Jesus bore his own cross. You'll notice it is never said 'he took it up'. The cross was what the world gave him. It is not a burden such as we all bear, and some of us have different burdens to bear; but the cross is the world's enmity to Christ. This was said next to the cross. It was the world's hostility and crucifixion of Christ that was robbing Mary of her son. It was fellowship in the cross of Christ that made John so suitable to take Mary.

You should remember also that the others had forsaken him and fled.