I believe that Jesus did not have a huge influence in his family, but two of his brothers did believe and follow him. James, the author of the Book of James and Jude,who wrote the Epistle of Jude, did believe. These two may not have been in the company of the disciples until after the Resurrection. They don't appear to have been numbered among the Disciples before the crucifixion. James was the leader of the Church in Jerusalem. Both James and Jude avoid claiming any special knowledge or privilege before God and the Church. In his letter James identifies himself simply as "a servant of God and of the Lord Jesus Christ." Likewise, Jude says he is "a servant of Jesus Christ and a brother of James." I assume that James was the second son of Mary and, perhaps, better known to the other disciples.
The Letter of James is a profound treatise on practical Christian behavior and service. The Letter of Jude addresses the problem of standing fast in the face of false teachings and doctrine. Both deserve close and consistent study, especially in the times we now live in.
I find it sad that it took so long for his siblings to come to understand who he was, but I value their testimony in the two letters attributed to them. The lack of family support may have helped prepare him for the rejection he received when the crowds turned against him after Palm Sunday.