Amy does take another big gulp from her glass, almost automatically, after River refills it. Unlike Rory, she's about as far away from sanguine over the fact that River is their daughter as one can mentally get. The emotional link isn't there for her; she hasn't yet lived through her sudden pregnancy and River's--Melody's--birth. Logically, she knows that everything she's been told makes sense, and that River and the Doctor might lie about a lot of things, but they would never lie about something as personal as this. She just... has an incredibly difficult time thinking of River as anything other than what she was before: a friend. An older friend. An older, intriguing, mysterious friend who was probably the Doctor's wife. And it turns out she was right about that--she just never imagined that River would also be her own daughter.

And she knows, on a level, that her difficulty accepting all this has hurt River. She can't help that. But she can help whether or not she keeps working towards acceptance. So she smiles at River, a lot awkwardly and uncertainly but with genuine affection, and says, "I would be, too."