@Ryuuji_Gremory Actually, you are already biased toward the second prince, as everything you said could be construed as the result of the second prince's propaganda. I am only saying that we (and the MC) aren't provided enough details to make an informed decision in the political environment, and the MC is already decidedly pledging his support behind one side. Don't forget, the MC is throwing his weight behind the second prince faction by only what the supporters of the second prince faction is telling them, in a way that its no different if the first prince faction come to him and told him how the second prince usurped the throne, being the second son, and have the MC join them in dethroning the second prince.
Just to break down some of your misunderstandings,
1. Why are you convinced that the members of the first prince faction are incompetent? Simply because that dickwad of a father was a member of the faction? If anything, the first prince's faction is the underdog, as the second princes' faction is likely larger and more powerful to ensure the second prince was the one who won the previous succession battle. We aren't simply told HOW the second prince won, and whether there was any underhanded actions involved, we simply assumed he was good because the second prince looked more charming than the first prince in the artwork.
2. By extension, why are you assuming the first prince's son will be incompetent and the second prince's son will be good? Because the second prince won the succession dispute of their generation?
3. They didn't invite any enemies, they hired mercenaries to fight against troops loyal to the second prince's faction. Don't forget, the second prince is the current king, his underlings controls the army, if the first prince want to have any change of winning a future for his son, he will have to either convince members of the second prince's faction to switch sides or hire mercenaries.
4. Once again, he is not "protecting the country", he is helping one branch of the royal family plot against another branch of the royal family in a succession dispute, with the only obvious reason of him joining the faction being that one faction has a guy he likes and another faction has a guy he hates. He was neither told nor understand which faction (if any) will be better for the country's future.
Don't forget, once everything settles, if the son of the second prince doesn't die, that son of the first prince will be the one who end up dead just so that the son of the second prince could seize power. Welcome to medieval politics.