Incheol's father was either exposed or framed for bribery, there's no way to tell and it doesn't matter because the outcome would be the same. His father worked for the previous leader before the congress woman, which means his loyalty is compromised. Usually the new leader will replace all the old high ranking public servant staff with his/her own people, so there's less chance of being betrayed (there's a chance the previous leader will try to reclaim the position or sabotage the new leader in some way).
Incheol's mother passed away.
I think Incheol's character is complicated in a sense that he knows what's right and wrong, but he's willing to ignore it in favor of gaining power. For example, the congress woman went out to dinner with someone from a construction company (Sinsheong is the name). This is a big no-no, as in government urbanization projects like these, many companies will compete with each other to be chosen by the government to be the one who build the infrastructures, so if the politician in charge shows any favoritism towards a specific company, that means he/she is usually corrupted. In Korean politics, contracts and bribery
are usually carried out during meals, so the fact that the congress woman was taking a meal with Sinsheong company...yeah.
As a citizen, Incheol wanted her to apologize and admit fault. But as an aspiring public servant, he gave her an idea to whitewash the incident by reframing it into something positive. Instead of saying "I'm sorry for colluding with private businesses for personal gain", she said "No contractor want to build in my district because it's not a big city, so I have to beg a big contractor to build by going out to dinner with them. It's not for me, it's for my citizens ". Incheol gave her that idea which helped her win the mayoral election. In reality, the congress woman is just another rich corrupted official (who's very terrifying in her own way, as she works like mafia).
The fact that Incheol knows what he's doing is wrong makes him feel guilty. He still has a conscience. His decisions directly led to the death of P's mother (he tricked her into handing the family's stamp seal which was used to sell their house away for the congress woman's urbanization project). P grew up as an orphaned and SA by the pedo policeman because of Incheol.
P.S: Not that Incheol wanted those things at the end to happen btw. It was an accidental consequence of his action. He felt very guilty about what he had done. This is a very good story is about how no matter what your intention is, your action will have real impact on others. Incheol's thirst for power will be confronted by P whose life was ruined because of him and the other adults in power.

His father was a type of high status public servant but got exposed for bribery, their family fell apart, parents got divorce (?), so he lives with his father. Now, where did the hate for Congress woman come from exactly? Was she in the opposition party of incheol's dad? Was she the reason his father got exposed? Or he just didn't like her ideologies?
Next, so his family falling apart was what made him want to be in poltics so he slept around with nepo babies or public figures to step on the ladder (?)
Incheol was in military force, does that mean he intended to be a public servant from a long ago? His dad's trasfer just fuelled it?
He then ended up working for the congresswoman even though he despises her ideologies and helped her flourish. So once he thought of fighting the politician and now he is fighting for the woman. Now he realises he has become the person he hated and doesn't mind it cuz he became power hungry, he wants to be in her place now that he is in too deep
Our pyeoghwa(sorry if I misspell) lost his mother and incheol is somehow responsible for it? P knows that so he despises all politicians/public servants (who doesn't?lol) ,also cuz his groomer was one, including Incheol(IN). Incheol doesn't know he is responsible (or doesn't acknowledge it) and devises plans to overthrow the female politician.
Now IN is just following his boss's order(to not breaknher trust )and obviously P is like a nuisance in his plan.
So when IN confront him, P puts IN in place (It feels wrong to call it sex )
Uh... Honestly, need to recap the first season