Just looking at their daughter's page:
"
Suetonius further claims that when playing with other children, she would attack them and try to claw out their eyes. This violence caused Caligula to state proudly that there was no disputing the girl's paternity. She was definitely his child."
and Caligula is apparently Scrooge McDuck: He also announced that New Year presents would be welcome on the first of January, and then sat on the palace porch and grabbed the handfuls and cupfuls of coins which a mixed crowd of all classes pressed on him. At last he had developed a passion for the feel of money and, spilling heaps of gold pieces on an open space, would walk over them barefoot, or else lie down and wallow.
and then

Although there is no accurate historical record, legend says that the 2-year-old Julia had her head smashed against a wall after attacking her mother's assassin by kicking and biting him.