Different situations lead to people revealing different facets of their personalities. From what we've seen of Twilight so far, she's always had to be in the leadership role, acting as the mature individual of the group and having to be a shoulder to cry on or bitch to. In those situations, of course she's not going to act like some giddy little girl, she knows better.
But here, we have a situation where there is no dire threat or glaring moral dilemma, Twilight is simply trying to turn a crappy situation into a fun one and do something she's never done before by engaging in something that's practically a right of passage for little girls, but something she never got to do - trying to reclaim something of a lost childhood, if you will. She's finally given a situation where she can let her guard down and just have fun, she she does so like a child because she feels that's how you should act in that situation.
As for her obliviousness to Rarity and Applejack's bitchiness, they're both her friends and she's probably giving them the benefit of the doubt that they wouldn't be so hateful to one another - unfortunately, she was wrong. It happens.
tl;dr: The characters are allowed to have a depth of personality, which changes as the situation changes. Doing otherwise makes them overly two dimensional.
Overanalyzing the ponyfolk in a pony thread: out new past time.