Let’s start with the first part of your question by reading John 19:25-27, “Now there stood by the cross of Jesus his mother, and his mother’s sister, Mary the wife of Cleophas, and Mary Magdalene. When Jesus therefore saw his mother, and the disciple standing by, whom he loved, he saith unto his mother, Woman, behold thy son! Then saith he to the disciple, Behold thy mother! And from that hour that disciple took her unto his own home.”  It is obvious that the Lord Jesus had tender compassion on His earthly mother before He died.  We can rightly assume that Joseph had died for Mary would have gone home to be with him after Jesus died.  At this point, the brothers of the Lord had no faith in who He was.  We read in John 7:2-5, “Now the Jews’ feast of tabernacles was at hand. His brethren therefore said unto him, Depart hence, and go into Judaea, that thy disciples also may see the works that thou doest. For there is no man that doeth any thing in secret, and he himself seeketh to be known openly. If thou do these things, shew thyself to the world. For neither did his brethren believe in him.”  In unbelief, the Lord’s brothers tempted Him to go to Judea and work openly.  They were not desirous of the Lord manifesting Himself in public, rather they were seeking to dishonor Him.

So, on the cross, the Lord would not commend Mary to go with one of His brothers, or sisters, because they were unbelievers.  Rather, the Lord commended her to the “disciple whom Jesus loved.”  This was John, the Lord’s faithful disciple.  While the Lord was accomplishing blessings for us, He also was aware of the needs of His earthly mother and sent her to live with John.  Then we read in verse 27, “And from that hour that disciple took her unto his own home.”  The last time we read of Mary is in the upper room with the disciples in Acts 1:13-14 where we read, “And when they were come in, they went up into an upper room, where abode both Peter, and James, and John, and Andrew, Philip, and Thomas, Bartholomew, and Matthew, James the son of Alphaeus, and Simon Zelotes, and Judas the brother of James. These all continued with one accord in prayer and supplication, with the women, and Mary the mother of Jesus, and with his brethren.”  Notice that the Lord’s brothers were also there with the other disciples.  Perhaps they were led to believe on the Lord because of His death and resurrection.

Now, let’s consider John 2:1-5, “And the third day there was a marriage in Cana of Galilee; and the mother of Jesus was there: And both Jesus was called, and his disciples, to the marriage. And when they wanted wine, the mother of Jesus saith unto him, They have no wine. Jesus saith unto her, Woman, what have I to do with thee? mine hour is not yet come. His mother saith unto the servants, Whatsoever he saith unto you, do it.” 

Turning water to wine is the first miracle our Lord did in His earthly ministry. (Verse 11).  If we look carefully, we can see the mother of Jesus approaching the Lord because, during this wedding feast, they had run out of wine.  Mary was acting as an intercessor between the guests of the wedding feast and the Lord.  The Lord mildly rebukes Mary by saying, “Woman, what have I to do with thee? mine hour is not yet come.”  The Lord Jesus did not need Mary to intercede between Himself and the others.  Mary graciously steps aside and instructs the people to interact directly with the Lord without her involvement.  Indeed, today, we take our prayers directly to God through Jesus Christ as we read in John 16:23, “Verily, verily, I say unto you, Whatsoever ye shall ask the Father in my name, he will give it you.”  There is only one intercessor, or mediator, between us and God…that is the Lord Jesus Christ.  1 Timothy 2:5 tells us, “For there is one God, and one mediator between God and men, the man Christ Jesus.”  (CC)  (641.6)