This, as well as its predecessor, would be so much better had they been combined. As it is, it just seems like you're saving face over a large grammatical error. Especially since Twilight can't see how the word is spelled.
"you're" and "your" are spelled differently, but pronounced identically. The two words are are hetrographs. It is incorrect to say "your" differently than "you're," it is only correct to only write "you're," differently than "your." It does not make sense that Twilight accuses Applejack of incorrectly saying "you're."
I agree with your general sentiment, but it's worth pointing out that they aren't pronounced the same except in a few specific accents that 'simplify' the sound of one or both. Common misspellings of that sort vary with the accent of the person writing them.