She did not do annulment of vows on the eve of Rosh Hashanah. So that does not apply.
On the side that this is not clarification of a mistake but rather a desire to be lenient with herself, would she need to do annulment of vows before a religious court of laymen? Or can she do something else?

Yes, preferable. They should be somewhat familiar with the laws of vows.

Her motivation is a combination of thinking that pants are modest and wanting to make things easier for herself. Does that fall under the definition of someone mistaken in Jewish law, so that she would not need annulment of vows?

On that same topic, can a woman appoint an agent for annulment of vows.

So maybe it is worth doing. Still, I am not sure it is required, since she did not actually vow or swear, and in practice she wore a skirt and not pants, which is a passive abstention. It is hard to say that three times she did not wear pants, because every woman sometimes does not wear pants. On the other hand, specifically according to your description, there are indications that she did this intentionally, meaning that she intended to take this upon herself, and perhaps even said so explicitly.
As for an agent for annulment, that is a dispute among the medieval authorities (Rishonim). The Shulchan Arukh rules that one does not do this, but the husband can serve as an agent.