Antipater wanted the throne so badly he was willing to destroy every member of his own family to get it. And for a while, it worked.
According to Josephus in Antiquities XVI, Antipater was Herod's eldest son by his first wife Doris, which made him technically first in line. But Alexander and Aristobulus, the sons of the beloved and executed Mariamne, were the popular favorites. So Antipater did what came naturally in Herod's court: he lied, schemed, and poisoned every relationship around him.
His method was brilliant in its simplicity. He never accused his brothers directly. Instead, he fed information to Salome and Pheroras, who passed the allegations to Herod as if they had discovered them independently. Alexander was supposedly plotting a coup. Aristobulus was allegedly telling people that Herod had no right to the throne. The accusations came from so many directions that Herod could not trace them to a single source.
Meanwhile, Antipater played the devoted son. He publicly wept over threats to his father's life. He surrounded Herod with loyalists who owed their positions to him. He even cultivated allies in Rome, spending lavishly on Caesar's freed-men to build a network of support in case things turned violent.
The strategy worked so well that Herod began treating Antipater as co-ruler, giving him a king's authority while his younger brothers watched their inheritance slip away. But Antipater had a problem he could not solve. The more powerful he became, the more the Jewish public despised him. They remembered Mariamne. They saw through the manipulation. And in a court where perception was everything, Antipater's popularity was a wound that would never close. His father's favor was absolute, but his father's favor was also the most unstable currency in Judea.