I don't know Gen kinda sus, I think he might be lying, like I'd understand that at the beginning they could have that kind of compensated relationship, but after so many years; I guess It could be explained that he gives her favours like giving Reiji a job after he graduates, but like how many favours can he really make; I'm under the impression that they are actually in a relationship, and the reason he gives here mother favours is because they are lovers. They all seem to have a weird obsession with Reiji, including the mother, more than just wanting him to support her in the house. They all have this need to posses him and his life, It's because they actually got no real chance to live unlike Reiji since he is a high school student with not much prospective in this town his future is an open canvas and could easily leave to find better opportunities outside if he wanted to. Meanwhile the mother and Gen can't leave even if they wanted to because on the mother's hand she has responsibilities to her ill mother and older son, and Gen has to carry on the family legacy of being the towns big shot, so he can't leave that easily. Haven control over Reijis future gives them an illusion of control on the future even if they can't decided their future they can decide his. So I don't know if Gen is actually gay for Reiji but I have strong reasons to believe that he lied to him and just is trying to guilt trip him into staying so that he can further control him (how he basically stated that he had a whole life planned for him) using the convenient fact that his father and here mother happen to be lovers. That would be more inline with the theme of all the characters that interact Reiji and their attempts to control his live and future in order to make up for the lack of control on theirs. The only one that is not trying to do that is the idol girl that is like just merely gave a suggestion but does not actively try to make him commit suicide (it can be argue that even Chako is trying to control him by, although a very sensible decision, not letting him kill himself or meet with the idol girl). Just like idol girl Reiji so far has no reason to live and is just letting himself get swift away by every other will; hopefully they both will find their reasons to live.