Maybe the dad have this mindset that would abandon and embarrassed to have sick kids? From my understanding, it seems the actual older son had weaker body and embarrassed to be even related to them that's why they had the 2nd son be presented as the older one and forgot about the weaker child. Of course as a mom, she wouldn't want to abandon her own, but maybe forced to abandon the weaker kid and forced to have the second child, the second child being a reminder to the dad's abuse so she, in her irrational mind, hates the 2nd son.
Also this is my just my theory of how things went down so just take it with a grain of salt.

this makes no sense so far. If both are legitimate kids then why acknowledge one and shun the other? it would only make sense if blondie isn't the father's son but no one talked about an affair