The way I see it, AJ's inner conflict in
The Last Roundup wasn't directly connected to
Parental Abandonment. It had nothing to do with her parents, it was all about making a promise and then finding out you're not quite good enough to get it done.
However, I do think it may be
tangentially connected. By which I mean not having parents around meant that she and Big Mac had to fend for themselves, and then care for two other people on top of that. From this comes a strong sense of self-reliance, which I believe results in AJ's "stubborn pride". But I don't think that label is quite accurate. I think it's more that because of her experiences, Applejack's sense of self-worth is rooted in being able to accomplish things by her own hand (er, hoof), and being able to support other people. If she has to rely on someone else, especially for something she really believes she should be able to do herself, then she's failed, big time.
And part of her character development is learning that sometimes, you
can't do everything by yourself. Sometimes the job is too big for any one person to handle on their own. Sometimes things go wrong, your plans fall to pieces, and your efforts are all for naught. Sometimes, you need to be strong enough to ask for help. As the saying goes, that's what friends are for.
There's no need to sharpen my pencils anymore. My pencils are sharp enough.
Even the dull ones will leave a mark.