I don't think Sophie being our sister would have to make Ophelia or Nana look bad or fake, but I will allow that the situation would indeed be messy.
Families are messy. Even the best families. Sophias family is far from the best.
There is very little Ophelia could do even if she's always know or suspected that Sophia was our paternal half sister, in that she knows or suspects our father is also her father.
Speaking to the toxic home life for Sophia and her family, Ophelia very likely might have thought she was doing the best she could to protect and help her granddaughter. Yes Annabelle is a brat, and probably abusive, but keeping Sophia and Annabelle living with Ophelia would allow her some influence and powers or mitigation. Getting Sophia taken off Annabelle, could get very messy, there being no guarantee she (Ophelia) would get custody and even if she did it would change little without kicking out Annabelle. Ophelia, for better or worse, wants or wanted to try and keep her family together and happy.
Ophelia would have little to gain, by revealing our father to also be Sophia's, especially if the case where the donation was while our parents were together and if our mom was unaware of it. Even in cases were there are no children involved, revealing someones partner to be cheating is always messy, and rarely turns out well for most involved including the person who took it upon themselves to reveal what was happening.
Ophelia saying what she knows or suspects could ruin two families, hers and ours. Not saying if she knew of "cheating" that she'd be right to say and do nothing, but I know many people would never get in between a couple when there's cheating. Knowing Annabelle's general attitude to men, if she were to learn the identity of her childs father and it was someone she personally didn't like, or perhaps hated, then she could take it out on her daughter.
As for Nana's "fake" personality, I don't think that would be true. We don't know, or I can't remember, when in the timeline Nana and Ophelia became friends. I don't see it as unreasonable that Ophelia often heard our fathers full name that regularly. In my experience people don't tend to refer to their friends and family by there full names, even when introducing them to strangers or other friends etc. If I was introducing a cousin of my to my friends I wouldn't use her full name, just her first name. "Hey guys, this is my cousin Sarah", they wouldn't know what her last name is unless they asked her or myself or if it otherwise came up in conversation. So to me at least, I don't see it strange that Nana could refer to our father nearly entirely by his first name.
We also, or again I can't remember, where we grew up prior to the accident that killed our parents, meaning depending on the timeline of events we, we being our parents and us, might not have been around Nana's town/village much. Easy enough for names and other details to get blurred and forgotten by Ophelia. Especially when as I recall at the start of the game, we weren't particularly close with Sophia despite her being best friends with our beloved cousin Cat.
And going back a bit, yes our parents are dead, so once they were dead, there was still no reason for Ophelia to dig up the issue of Sophia's father, and who he might be. Everyone would have already been dealing with a lot at the time, and it would get harder and harder to find a reason to mention things as time went on.
I can't remember all the other points to refute them all, but I don't think Sophia being our half sister would cause too many problems if handled well. No character assassinations required
