Fridge Brilliance: Why does Jacen become so out of character compared to his past self? Because the Light Side is associated with reason, control, and compassion to channel the Force. The Dark Side is associated with emotion and release of control. As Jacen leans towards the Dark Side, he thinks less clearly and becomes more impulsive due to the resulting lack of self-restraint.
This is shown in both subtle and overt ways. He muses that he prefers the company of droids because they lack independent motivation, and dislikes aliens because he finds it hard to to read their facial expressions. Also, like most Dark Siders, he becomes very self-absorbed and loses the ability to examine the universe from other people's points of view. This culminates in a Vader-like breakdown where he kills a loyal officer who failed him on the bridge of his ship in front of other crew members.
Luke considered his childhood on Tatooine to be incredibly boring, while Mara was raised from an early age to be an assassin and espionage agent. Thus Mara probably figured that Ben's "internship" with Jacen in the Galactic Alliance Guard was pretty normal and Luke just figured his son was getting a more interesting childhood than he himself had. Hence the amount of time it took them to figure out that the whole thing might not have been the best idea.
The Jedi, the Alliance government and the military might have thought that Daala would be an ideal "peacetime president" since, despite what Invincible would lead readers to believe, she has historically been a General Failure and most of her military campaigns have ended in crushing defeat for her side. Thus they imagined she had little potential to successfully start any serious wars that would not flame out pretty quickly.
There's also the fact that, to the greater galaxy, it has been decades since the last time that Daala threatened the galaxy. Since then, there's been the Yuuzhan Vong invasion steamrolling the New Republic, the crisis with the Killiks and the Chiss, and a civil war that landed a Sith Lord in the office of the Chief of State. Daala's activities against the New Republic happened long enough ago as far as the general public is concerned (especially given that her attacks were very localized, more against singular planets, Mon Calamari, Khomn, and Yavin 4, than the New Republic as a whole), that she is the lesser of various evils after a whole host of really crappy options leading up to her election.
Fridge Horror: For a good chunk of the mid-New Jedi OrderWarmaster Tsavong Lah was trying to arrange for Jacen and Jaina to fight to the death as part of the Yuuzhan Vong's ritually mandated Twin Sacrifice. In LOTF, the Vong ritual doesn't happen, but the twin duel to the death sure does. At the end of Invincible, Jaina wonders if Jacen didn't really win after all, but in at least one sense the real villain who wonLOTF from beyond the grave was Tsavong Lah.