Tiberius Claudius Nero was nothing like his suspicious, tyrannical son.
Born in 85 B.C. he was a member of the Claudian family. He was a supporter of Julius Caesar and after he had served as quaestor, Caesar sent him to command his fleet in the Alexandrian War. Tiberius did very well and the battle was won so when he came back home to Rome, Caesar made him a priest (do not think of Christian-style priests, this is more of a political position) and then sent him off to set up colonies in the Roman provinces, mainly Gaul.
After Julius Caesar was assassinated, Tiberius called an amnesty in order to stop senators quarelling with each other and was later made praetor.
As a supporter of Julius Caesar, he was on Mark Anthony's side and not Octavian's. His dislike for Octavian was about to get worse though. In either 43 or 42 B.C. Tiberius married Livia who was also his cousin (this may explain why Tiberius, Caligula, Claudius and Nero were all rather unhinged, so to speak, as they were all directly descended from his union with Livia).
Having Octavian as an enemy forced him and his young wife to live a life on the run for three years. When Livia got pregnant for the second time they decided to return to Rome with their 3-year-old son Tiberius (the future emperor). However, when Octavian met Livia all hell broke loose as he fell madly in love with her and wanted to possess her by any means possible. He made no point of hiding his passion for Livia and many scholars think she may indeed be the woman Suetonius says Octavian grabbed duing a banquet and dragged into a nearby room with great urgency. The account says the woman's husband was present at the banquet but obviously Octavian's passion was so great that he did not care about this at all. A while later, the woman is said to have emerged from the room in a dishevelled state and red with embarassement...
Poor Tiberius was now about to lose his wife. It is thought that Octavian applied pressure on him to divorce Livia because on the very same day the couple got divorced, Octavian married her. Shorlty afterwards, in January 38 B.C. Livia gave birth to her second son with Tiberius, Nero Claudius Drusus.
For 5 years until his death in 33 B.C Tiberius raised his sons on his own. When he died the boys were sent to live with their mother and stepfather.