Did Jesus allow his brothers to be unbelievers?

I was thinking about the Biblical book of Jude and its probably human authorship by Judas the brother of Jesus Christ. We know that Jesus' brothers did not believe in him early on in His earthly ministry as John reports in John 7:3-5. It also seems possible that His brothers were absent at His resurrection, as Jesus gives to Mary the Apostle John as a son (John 19:26). That point may be questioned as no others seem to be present at the crucifixion and we know that most ran away. Certainly following His ascension, there were His brothers, James and Judas, with the Apostles (Acts 1:14).

So, now the theory: The Lord did not bring His brothers to faith during the time He walked the earth because they would have led people to speculate that He was just a sham who had recruited His brothers to act like disciples.

What I am not saying:
- Jesus brothers were at risk of being lost, for Jesus knew they would live to the point where they came to faith.
- Jesus was being deceptive.

When I presented it to my Bible Study class the above objections were raised. Also it was suggested that Jesus would be taking away their free will. That can be dismissed with the proper understanding that, though we have free will, our sinful nature will only choose to disbelieve in Jesus unless the Holy Spirit acts upon us.

Why would Jesus behave according to my theory?

1. As stated above, He would have a more believable group of disciples if they didn't include the easy-to-recruit brothers.
2. Have nay-sayers in His own family kept Him from being an "easy sell" to believe in. Stated in an extreme case, if nearly all people believed in Jesus, wouldn't you find yourself compelled? That would be belief via the law - being forced to believe. Instead, Jesus comes to us through the Gospel.
3. There was able to be a more dramatic reversal for His brothers, from unbelief to belief. James became a pillar of the Church in Jerusalem and wrote the book of James. Judas wrote Jude.