In today's passage, we read about how Paul's nephew hears about the plot against Paul and averts Paul's certain death. We don't really know a lot about Paul's family - it's a lot of guesswork from just a few passages, but here's some of what I could turn up:
"It is unclear how many of Paul’s family members were in Jerusalem (vv. 17, 22). The term “son of Paul’s sister” could indicate a man in his twenties or even older, although it is possible that he was younger (see v. 19, where the commander took him by the hand). It is likely that Paul’s sister also resided in Jerusalem. The fact that this relative of Paul may have been present during the plotting against Paul’s life (the grammar can be taken this way) has led some scholars to wonder whether Paul’s family itself may have been strongly opposed to him."  (emphasis mine)
"At this stage Paul’s nephew enters the story with his tip-off to Paul (23:16). He was able to get in touch with Paul and even with the centurion because Paul was an unconvicted Roman citizen and had to be treated with due respect. When Paul said that he lost all the things that he could claim from a human standpoint because of the gospel (Phil. 3:4–8), this must have included his family. His father, probably a wealthy person, likely disowned him. But something of family affection must have remained for his sister’s son to take the risk of spilling out the plot of this murderous group."  (emphasis mine)
Based on what we know from this story - that his family knew of the plot - and the fact that Paul went from extreme persecutor to missionary, it's pretty likely that Paul's family was set against him. Jesus said this would happen - as we talked about before, Jesus divides people. He causes the rising and falling of many. Paul frequently talks about the physical trials he had gone through, but it appears that considering "everything a loss" for Paul most likely included his family as well.
 Ajith Fernando, Acts, The NIV Application Commentary (Grand Rapids, MI: Zondervan Publishing House, 1998), 577.