I think that woman in his flash back was perhaps his girlfriend/wife/Yuki's mother,because that woman and Yuki closely resemble eachother.

Maybe before she got turned into a vampire,she gave birth to Yuki.We dunno if half-vampires can exisit yet so I can't say.
I'm also wondering if she's still alive even though Yuki said her parents were dead [did she? O.o] or maybe she died so the Headmaster wants to fulfill her wishes.

Just throwing some thoughts around.