When Herod the Great became seriously ill, the Roman studies of the Jewish princes
came to an end. At the end of year 5 or the begin of 4 BCE the princes and Jesus travelled to Judaea. In 7 BCE, as the conjunction of the planets Jupiter and Saturn announced to the astrologers a change of ruler in Palestine, they fortunately stayed in Rome and so escaped the distrust of Herod the Great in his old age.
Two half-brothers of the princes, the sons of Mariamne, Alexander and Aristobul, were out of luck: Herod had them executed for flimsy reasons in 7 BCE. In the gospel according to Matthew this episode turned up as the massacre of the infants of Bethlehem, Matt 2, 16-17. There Jesus escaped the massacre too, this time because of the flight into Egypt (= Rome).