Thanks for all the responses. My main interest right now is John 19 and what would be the customary course of action for what to do with a widow. The Fourth Commandment is a good starting point, but I hope there is something more specific.
One passage that comes to my mind is 1 Timothy where St. Paul speaks of the treatment of widows. It could be said that Jesus entrusting Mary to John would not have happened if Jesus had any siblings sill alive.
"But if any widow have children or [descendants], let them learn first to shew piety at home, and to requite their parents: for that is good and acceptable before God." (1 Tim 5:4)
One point of disputation could be that the KJV renders the word ἔκγονα, which I replaced with "descendants," as "nephews," so therefore, if John implies that Jesus had no surviving siblings, he had no surviving cousins as well. However, Strong's indicates that cousins is an inaccurate translation of ἔκγονος.
It could be said against this that John also wrote:
"For neither did his brethren believe in him" (John 7:5).
Thus, since his siblings showed no piety toward him, why should they be expected to show any piety toward his mother? However, this is not convincing to me since if he had siblings, they should have had plenty of evidence that they ought to believe in him.
So I wonder if there might be any similar passages from the Old Testament or maybe rabbinical literature that deal with this specific sort of situation.