That would explain why Youki disappeared all of a sudden. Theory : he cheated on Yuyuko, so when she discovered it, she banned him, but kept the child as a servant/confident/friend/whatever. After that child grew up and had a daughter on her own, something bad happened, and Youki temporarily came back to teach Youmu, before leaving again.
This is an alternate timeline; Anything that happens in this plot explicitly has nothing to do with any sort of retelling of the "canon" plotline. (Even though all fanworks aren't canon by definition, anyway...)
According to standard Stargate Parallel Universe rules, you can end this plotline with everyone dying off except the one character from the "real timeline", (or even blow up the whole Earth,) or else pair off everyone in whatever wacky romantic pairings the author wants.
Nitori/Yukari pairing FTW.
Punish him later.Be careful.Sakuya-san!Are you alright, Yuyuko-sama!?Eee, Youki!Th-thank you very much...Interesting...But it looks like some skilled types are mixed in among them.You give me such trouble.You're not too bad.Honestly.Hyaiiiii!Look at that, going all gooey immediately...