Source.
I think I've got a handle on the way Amy might view the Doctor. He's that amazing, gigantic, vaguely scary but brilliant older brother who abandoned her when she was little, leaving her fixated on this ideal, this dream of a man who might just have made her life wonderful had he stuck around/come back. Then he did, but far too late for her liking, so she wacked him 'round the head like any good little sister. She's mad, intelligent, isolated, but human, like that less adored younger sibling of an overachieving, amazing older one. She'll run around in cahoots with him, but the minute she breaks his rules, the rules of the older kid, there's hell to pay, until she makes him remember why he came back for her in the first place.
I'm coming at this, of course, from my very Supernatural-based experience of viewing television texts, which means I'm always going to look for the unconventional, powerplayed sibling/BFF relationship, whether it's Sam and Dean, Pam and Eric, Effy and Tony, Chuck and Bryce, pretty much any two kids on Gossip Girl, but most especially Chuck and Serena, Eliot & Parker & Hardison, the Boleyn girls, Camilla and Charles from The Secret History, and so on.
Eleven and Amy aren't, in any way, manner or form, close in the way siblings are, yet. There's a touchpoint, early in both their respective current lifetimes, and now they've clashed again. Amy feels like she has some claim on him, with his broken promise, the ideal of the Raggedy Doctor, which has seen her conceptual fixation on him grow in leaps and bounds, just like that for a runaway big brother might, especially in the absence of any other kind of caring family.
So they'll fight, lie, trick and generally run around each other while having the time of their lives, because with siblings, it's always a competition, always trying to maintain or upset the status quo, but with natural, chaotic rhythms of talking and understanding each other that run through it all.
With the TARDIS as their sentient clubhouse.
At least, that's what I hope to see.
Also: look, I know the Doctor's imprinted on Jack ever since Nine, but really, this is a little less than subtle, costume director:


Just sayin'.