During "Pinkie Apple Pie", it was revealed that Pinkie is possibly related to the apple family. When Pinkie told them all that she might be their cousin, Apple Bloom was jumping up-n-down the house yelling: "I GOT ANOTHER SISTER! I GOT ANOTHER SISTER!"

So here is my question: When AJ had to go to Manehatten, why didn't Apple Bloom ask Pinkie to be her sister for the social? I know the most likely answer that she didn't thought about it or she really want to compete with Applejack. I just saying that Pinkie Pie would most definitely accept an invitation like this and can without a doubt act like a sister.

4776787 Pinkie Pie is more of an organizer. Remember the Summer leaves running competition? Pinkie Pie wasn't in it. She watched (and commented) from afar.

4776787 Apple Bloom had been practicing with Applejack. That's what she wanted to do. And the focus of the episode was the brother/sister bond. Once Big Mac found out about this, she wouldn't have asked Pinkie, because he really, really wanted to help.

Not to mention that during that episode, we never really found out for sure, and they agreed they'd keep it among themselves. So if Apple Bloom asked Pinkie on the grounds that she's a relative, everypony would know she's a relative, wouldn't they?

4776787
Maybe Bloom realized, at some point, that she's probably more closely related to half the ponies in Ponyville than Pinkie Pie.

But really, actual blood relation doesn't seem to be all that important. She could have asked Pinkie. But she could have asked anyone she was close with. Whomever that is. Zecora, maybe. After all, Scoots was with Dash. No relation.

4776787 Probably because Apple Bloom didn't think about that possibility, she was too upset about the fact that she couldn't compete with Applejack.

All that said (and this probably goes without saying itself), it certainly sounds like a good writing prompt. This could probably make a good alternate-canon fic if done right. I believe given the right circumstances, AB and Pinkie would compete together.

4777167 I think the bigger question is, why didn't Sweetie Belle look into possibly competing with Fluttershy or Twilight? I'm sure either one of them would've volunteered in a heartbeat (Twilight especially since she had nothing to do).

4777171

Those seem a bit far-fetched to me, at least in my imagination. But the only reason for that is because Sweetie Belle didn't seem nearly as distraught that she couldn't participate. She seemed more upset by the fact that Rarity couldn't make it, more so than the fact that she couldn't compete in the event itself.

That said, I feel like Apple Bloom was upset by both facts: that Applejack couldn't go with her, and that she couldn't compete period. Strong as her bond is with Applejack, she's also got a competitive spirit – more so than Sweetie Belle – which makes me feel like she would've been more receptive to the idea of having a replacement than Sweetie Belle might have (especially given how things played out during the last Sisterhooves Social).

4776787
As others pointed out, I think Apple Bloom was less concerned about the competition itself, and more concerned with not getting to do "fun thing with big sister AJ."

Big Mac stepped in to help, somewhat missing the point. Well, not entirely, because he wanted to spend time with his little sister and bond. Which was exactly in the spirit of the competition, and why nopony else had any problem with him entering.

AB might have been excited in Pinkie Apple Pie about having a new family member, but it doesn't seem like she would have thought of asking Pinkie for this on her own. However, if Pinkie had overheard, she could have volunteered and I think AB would probably go for it and enjoy herself. But that would be an entirely different story than the Big Mac-focused story we did get.