When we first meet the Nero and Elizabeth, one of Apollo's thoughts was that he prefers to follow his mother's style of ruling, which is fair but strong. However, she can be dangerous when provoked (esp. if Apollo is in danger), which is why the samurai ends up in prison. She also humiliated Caligula for days in a packed Throne Room because he convinced Nero to withhold anesthesia from Apollo after his whipping in the Colosseum.
Part of the reason Apollo is so weak is that the paranoid Nero feared him too much to prepare him for rule. Apollo banishing his mother later in the story is just an excuse to allow her to go to New Bethlehem and secretly negotiate for peace with the Realm. The concept of a fake fallout between mother and son is right for the story, but I still don't like the way it turned out in v3.
At first, Apollo continues following her style of leadership, which is why he tries not to act violently in response to what's going on around him. However, like you said, he orders a hit on Nero and tells his aides he may execute Mama (because he knows too much about the hit). The hit was something Apollo felt forced into after Nero's first attack on New Bethlehem. Apollo also orders the failed commando raids to arrest Admiral Lupus and Governor Hadisius.
After the 2nd (final) battle at New Bethlehem, he decides to force all of the senior officers (those promoted by Admiral Lupus) out of the Praetorian Fleet and scrap the Praetorian flagship altogether. He's also going to do a purge of senior officers of Earth's home fleet, which was commanded by Governor Hadisius. Hadisius fled the battle, but Apollo expects to capture him eventually and execute him. He also banishes Caligula from the Imperium forever, providing him with nothing more than an explorer ship that will allow him to flee to distant outposts in the galaxy, where Realm bounty hunters are sure to pursue him.
So, you see, there is a progression from weakness to strength forced on him by circumstances. Assuming I ever finish the story and write book two, it was always intended to be much darker. Joseph will be haunted by his guilt for unintentionally triggering the destruction of New Bethlehem, and Apollo will pursue galactic colonization and the Imperium's conversion to Christianity aggressively.
If there's a book three, it was originally intended to be an upbeat ending where Joseph and Apollo together discover the dying alien race that has interfered with the human race in a game of galactic chess (hence the reason there are two versions of God), responsible for the rise to power of Alexander the Great, Stalin, Hitler, etc. The last scene was intended to be the two dying aliens saying to each other they have time for one more round before their deaths.
Since I'm going to use Dr. Francis in the year 7329 to interfere with the human race in 4017, there's no need for the aliens. I may write the second, dark book (set in 4021) and then jump forward to 7329 where the descendants of Joseph's fanatic followers attempt to overthrow the galactic government. The story set in 7329 is the one I tried to write first, but eventually came around to Joseph & Apollo first.