Amy Pond was never a character in her own right.
Throughout the series, she represented many things. She acted as the "strong female character," paying lip service to ideas of female independence, intelligence and sexual liberation. She was a vessel through which the writers could present or explore the theme of the week. She never maintained an interest in anything, forgot to care about things she was passionate about the episode before, and had only had one consistent trait or interest: her marriage.
She was, in short, the Strong Female Character (TM) in the worst kind of way. She was all "strong female," and not enough "character."
Amy Pond seemed so promising in her first episode. She was the "girl who waited," who saw the Doctor when she was young and alone and waited for him to return, through disbelief and psychiatrist sessions and (most likely) constant concern that she was insane after all. She didn't fit in. She had no career ambitions or close connections, so she worked as a kissagram, earning money by taking on different roles and changing herself to please over. And then, over a decade later, the Doctor reappeared on the night before her wedding and offered her all the adventure she never had.
So far, so good.
Unfortunately, even this compelling beginning was completely ret-conned by the end of her run on the show, when it's revealed that the Doctor visited young!Amy the following morning and promised that he would return, and that she would have adventures, on older!Amy's orders. The one defining, concrete thing about her character -- that she was abandoned by the Doctor as a lonely young girl -- completely disappears. So then who is Amy Pond, this woman we've seen for the past two and a half years?
Well, she's Rory's wife. And that's about this. Her emotional dramas, the circumstances of her departure, are all built around this fact. (She also has trust and worship issues with the Doctor, but the cause of those was seemingly ret-conned away). Her wife-ness really is her defining feature. Her emotional arc in her first season is, in short, "do I want to get married?" The first episode implied, at least to me, that she didn't, because she had always settled in her life, and she was finally getting a chance for adventure. But I was wrong there. The answer, simply, is yes. She does want to marry Rory. Her ensuing drama is about who loves the other more, whether she is pregnant or can even have children (but not about the lost child she does have), and other Rory-related issues. Indeed, when the Doctor wants to release his hold on her and signify that she has grown up, he calls her "Amy Williams."
But her status as a married woman is not enough to carry a plot or show that she's a "strong, independent woman," so the show also gave her attributes that changed seemingly every episode. She loves Rory fiercely, except when she's trying to seduce the Doctor or get him to kiss her at her own wedding. She will do anything to protect her daughter, unless that would disrupt the fun of the episode. She has childhood friends that appear out of nowhere, and jobs and interests (modelling! Writing!) that seem thrown in simply to give the illusion of interests and depth, without any continuity or development. Sometimes, she is the sassy, can-do companion who can work in the Doctor's stead. Other times, she is the damsel in distress to show how heroic and capable the Doctor is. Unlike Rory and the Doctor, she rarely speaks to characters-of-the-week, unless it's specifically to make a point about how she is a Strong Female Character (see Dinosaurs on a Spaceship). One major exception that comes to mind is her interaction with Vincent van Gogh -- a truly wonderful episode that still relies on a trait (Amy's love of art and van Gogh in particular) that never appears before or since.
After two and a half years, we know less about Amy Pond than we did about Rose, Martha or Donna in their first episodes. In fact, due to ret-cons and time manipulations, we actually know less about Amy now than we did about her in her first episode. Who are her family? What's her relationship with them? Who are her friends? What are her dreams? What is she unsatisfied with? Once we disregard the no-longer-true details revealed in the first episode, we're left with one compelling answer to each question: Rory. It is all Rory.
And that's why we don't see what happens to Amy, or what her life involves, after she blinks and is sent back in time to her husband. As long as we know they're together, there's nothing else to say.