It's like these characters would rather feel angry and sad at each other than forgive each other and move on.
Sadly, that's a pretty common thing for people who are under a lot of stress. As I understand it, being able to lash out and hurt others releases pent up stress and gives people a sense of control in a situation where they feel like they have none. Or so others tell me...I've certainly never fallen into that emotional trap myself. Nope, perfectly rational being for my entire life.
Which one first? Additive and then multiplicative, or multiplicative and then additive?
Both. Simultaneously.
On a more light hearted note than destruction of familial relations, the bloodline that the woman Orochimaru found perfectly explains Hidan. No need for Jashin to be real messing with the world by giving this guy superpowers, he just has a bloodline.
Tinfoil hat time: Oro created Hidan.
During the Iron-Liberator arc, Jiraya said that Oro knew that he had to keep a low profile (when he was a missing nin) in order to not be dogpiled by everyone. So if Oro wanted an S-level nin that he can manipulate and direct, that's a proxy preventing people from knowing that it's Oro pulling the strings, an immortality bloodline would be just the thing to produce such an S-level nin. Note that Hidan doesn't seem to have a lot of social skills, long-term planning skills, or patience. All things that make Hidan easily manipulatable to someone like Oro.
I think the ages even work out. The sannin are 50-60ish, right? If so, assuming that Oro found the woman in his 20s, that would give Hidan an age range of 20-40, which seems very reasonable.
Granted, I think this probably didn't happen (even though it would make a lot of sense and make Oro more terrifying [which is always the real goal]) just for the doyalistic reason that SV might not allow that.