I still have a sneaky feeling from the way the Doctor responded to the news that River = Melody that She is also his Mum. "How do I look?" And there's a neat mid-way solution to the thing about him being 'half-human'. And it would explain why she knows his name.
I highly doubt that they would go down that route. After all the flirting, innuendos, and the kiss, it would be about 10 levels of
ick beyond anything Luke and Leia did!
What I can see is that through some wibbly-wobbly, timey-wimey stuff, that she is the Doctor's once and future wife. What I mean by that is that she is Susan's grandmother. Not sure exactly how they'd explain that, but if River is a human/time-lord, which seems likely, then maybe she somehow ends up being the mother of Susan's father or mother. Susan is something that they've never really touched on in the new series, and when they do skirt around the issue, it's always met with what seems to be sadness and regret. Maybe he found Susan somewhere on one of his early, unseen adventures and figured out that she was a direct relation, but never really knew where she came from?