This is a very sweet and under-appreciated moment — a romantic date for her birthday. Ice skating and a personalized concert. Can you imagine The Doctor Ice skating? And he brought Stevie Wonder out of his own time just to sing for her. No chasing down Sontarans. No trying to save the universe. No drama. No tragedy. Just a cute romantic date with his wife.
I’ll also point out that River knows who Rory is at this point, even if he doesn’t, and she’s telling him all about her date.
River didn’t grow up with her parents. She didn’t get a Mom or Dad asking her about her day, and she didn’t get to gush to them about her petty troubles or love life. But she gets this moment. She comes back from a perfect birthday with her husband to find her father waiting. And for once, she gets to tell him all about it.
I like to think of this as River saying “You don’t know who I am, but I want you to know that I’ve turned out fine. I’m in love, and yeah, he’s insane. You know that. But I’m happy. I’m very happy.”
As screwed up as their relative timelines are, as broken up as their family is, River manages to tell her father that she’s okay, more than okay, despite everything.