"In Matthew 12:46-50, Jesus acts like he didn't care at all about his own family. Is that true? I would think that the distance and time He was away from his family would make him anxious to be with them."
First, as a Hebrew man (and a perfect man at that!) Jesus would have been respectful and loving toward his family. He would have perfectly obeyed the 5th commandment to honor his father and mother. When you think about it, the Gospels tell us very little about the daily life of Jesus. The stories in the Gospels skip from one incident to another without filling in the gaps. There had to be plenty of times when Jesus visited his family and did the normal things that Jewish families do.
On the other hand, he was a man on a mission. At times (like in Matthew 12) he was so focused on his mission and so dedicated to God that God and the mission took priority over his family. After all, remember that Jesus said, "If anyone comes to me and does not HATE his father and mother, his wife and children, his brothers and sisters - yes, even his own life - he cannot be my disciple" (Luke 14:26). That's not to be taken literally -- we are not literally to hate our families -- but it does mean that God comes before our family. Jesus interprets Luke 14:26 when he explains, in Matthew 10:37, "Anyone who loves his father or mother more than me is not worthy of me." So by his behavior, Jesus was modeling what it means for us to pick up our cross and follow Jesus.
The other thing Jesus was doing in Matthew 12:46-50 was
showing how much he loves US. He considers us his family, just as if we were
his own literal mother, brothers, and sisters. So that's pretty cool that
Jesus would claim us for his very own like that.