At first, I thought Vin's unexplained power came from her earring—that the truth behind her power was simply a mingling of Feruchemy and Alomancy. It seemed likely. If the Lord Ruler was able to increase the power of his Steel-Pushing by this uncanny mingle of genetic magics—making him capable of touching metals inside the body—I assumed that Vin Pulling the Lord Ruler's bracelets out of his arms was done not from the mists, as she had thought, but from the unknown power stored within her earring.
But, after rereading Mistborn: TFE, I realized this wasn't the case. When Vin attacked the Lord Ruler, he had already Steel-Pushed her earring from its place. It was only then that she was able to draw on the mists.
But does this mean she doesn't have Feruchemical abilities? I don't think it does. It simply means that she has another power—a fourth power, perhaps—similar to that of the Inquisitors, except that she's also able to draw upon the mists. From what I can see, the Inquisitors can't do that.
So what does this mean? It's possible that Vin not only has three powers—as you suggested—but four. Perhaps the stud in her ear gives her the extra boost she needs to pierce copperclouds, like the Inquisitors. Perhaps not. It's possible that Vin's earring is a Feruchemical store, and that it is what allows her to pierce the clouds. Perhaps it's a little bit of both.
This is, of course, pure speculation. I haven't read any annotations, so I'm not up to date on all the possibilities. I do not, however, believe that Hemalurgy—what the Inquisitors use—is the same power Vin uses to draw from the mists. It just doesn't add up for me.
