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Intertigo is common when skin folds rub against each other. It sounds that you diagnosed your aunt correctly (I think you know more medical stuff then some of the people I work with). I have never used or heard anyone use cornstarch for intertigo. What I would recommend is washing and drying as you already have, applying Hydrocortisone cream 1% (available over-the-counter) and putting some baby powder on.
Sometimes yeast can grow in the areas of intertigo but usually when yeast is present you see all these small red dots around the redness, they are like little satellites all over the place. It doesn't sound that your aunt has an infection. The oozing is probably just due to really bad skin irritation.
Again, what you did is right (except for the corn starch, I cannot say anything about that). Keep the area open, apply small amount of Hydrocortisone cream and put baby powder over it (if you have it, if you don't, not a big deal). That's all you can do. Of course, she will need new Depends so that this doesn't get worse or continue to happen.
But Hydrocortisone usually takes care of Intertigo within a couple of days. I doubt that your aunt will develop a yeast infection there.
You are doing correct by letting it air dry. If you have to put depends on tonight and don't have the medium size, you can put some vasoline on the raw area, cover it with 4x4 or 2x2 gauze and put the depends over it. You can use Hydrocortisone 2 or 3 times per day.
I don't know anything about corn start properties but this is good to know. I will keep it in mind for the future.
It doesn't sound like your aunt developed infection so dont' worry :)