Queenie, this is good. I mean really good. I like the way you dive right into the meat of the tale and show the conflicts in both Claire and Hao, including the conflict between them which both are trying to resolve. And her veiled golf hint to him later shows that she understands the political situation she's in better than he does.
But it feels like a vignette from some larger, unfinished narrative arc. We're all assuming some of the backstory from the context, and we night or might not be right.
For example, is Claire fully super-powered or just partly? She seems to be fully powered, but we don't really know. How long has she been in China? (Is it still called China?) Seems to have been quite a few years. Why are these assumed descendants of Superman being treated as property? (From the opening scene, that's not an assumption). Did one of the earlier Kryptonians turn Darth Vader on the world? Or are these the descendants of Nor's invasion force? How are they being controlled? Claire doesn't seem to be in any immediate danger, and there's no hint of such danger to her family. She even says plainly that she feels no allegiance to her former country - and we don't know if that's the U.S.A or not, although it's definitely implied later. Why did she and the rest have to be "liberated" from the U.S.A anyway? Was there some kind of global conflict or economic or political collapse? She's obviously being induced to mate with (or at least pair up with) a military man - nice promotion, from lieutenant to general - and she's not really free to choose the guy. Is she in contact with other supers in the world, or are they all living pretty much solo lives? I know she's spoken with her brother, but it seems that it's been a while and he's apparently not sharing everything with her. Is Claire's situation unusual or are all the supers in the world now some nation's slaves?
So many questions, so few answers. If your muse(s) prompt you to expand on this unusual (if slightly dystopic) world, I'd read it. I'd even be willing to beta it for you if you wish.
One more thought. When I read the name "Song" I immediately thought of River Song from Doctor Who. May I place Alex Kingston (the actress who played the character) in Song's role in your tale? I assure you that I intend that to be a compliment, and I hope you accept it as such.
