This is what I think happened in the past:
1. MY's mom was INSANE. like literal psychopath and she tormented her daughter and her husband for years driving them both crazy.
2. MY's mom killed KT's mom. maybe kt told his mother about MY and she went to talk with her mother but ended up killed or maybe MY's mom hated the boy and wanted him to leave her daughter alone (most likely) and had a fight with KT's mom and killed her.
3. MY's father found out about the murder which only fueled his anger and craziness so he:
a- kills her
b- thinks he killed her (maybe he had a fight with her and she fakes her death to escape him and the murder all together - or he wasn't even close to killing her but his poor mental state made him believe he did)
4- he hates his daughter bc she's a younger version of her mother (as the mother herself stated before) and he tried to kill her too either because he thought she was his wife or because he thinks she'll end up like her.
5- when KT's mother was killed it's either the killer or her husband that ST sees (he never met MY's father as of date so we don't know how he'll react if he saw him) but my bets are on the mother because the butterfly thing whatever that is suits her personality better than the man.
6- I don't think that the woman in the hospital is MY's mother but I do believe that she is alive. though I can't rule out the possibility that she is that patient because it's a very good plan to fake losing her memory and go to the hospital her husband is in to torment him even more and make sure he won't tell on her if she decides to reveal herself once again to her daughter or the public (considering he's the only one who knows about the murder)
that's all I have I guess please discuss your options and theories with me I'll appreciate it a lot <3