Darach and Caitlin were first introduced in Platinum's Battle Frontier as the Castle Butler and the Lady of the castle who overlooked these events. It was quite strange to have both their sprites appear together when you battle the Frontier Brain, yet are only battling Darach.
We learn from an NPC that Darach had emotions for Caitlin but he does not show it.
We learn more about Caitlin in BW:
BW Text Dump
Judging by her dialogue and affinity for Psychic Pokemon, I believe that Caitlin herself has psychic powers, but the way she talks, I believe her psychic abilities have the potential of being greater than even that of Sabrina.Elite 4 Battle (First Round)
Caitlin:...Whenever I battle, my emotions are rattled.
She who ruined all that around her whenever she evoked her power is no more now...
And yet, still...
My ideal is to wake up to an elegantly-earned victory.
You... May you continue to be my companion in battle... or otherwise.
Caitlin's Villa (Spring)
Caitlin: Things always turning out the way you like is a precedent to unhappiness.
There are things I can and cannot do. Recognizing that is key.
There was an annoying person who said that long ago...
Caitlin: ...If one's psychic ability were truly uncontrollable, one would be better off without it.
Elite 4 (Rematch)
...An inexperienced soul runs wild with its power.
There were some days on which I was prohibited from battling...
That same soul that yearned for battle dances at times like now...
Furthermore, her powers are closely tied to her emotional states. She talks about how battles rattle her emotions, then goes on in to talk about "she who evoked her power" and ruined all that was around her being no more.
She also talks about how it would be better off to not have psychic powers if it were uncontrollable, and how an inexperienced soul runs wild with power, then goes on to talk about how she was prohibited (not unable) to battle in the past, but which her soul dances happily now.
I believe that Darach was assigned to Caitlin by her parents to teach her how to control her emotions by removing her from the battle field and battling on her behalf. Darach wasn't battling for Caitlin because Caitlin was unable to, but because it would be too dangerous for her to do so. He had feelings for Caitlin, but knowing that her abilities were tied strongly to her emotions, chose not to speak of it so that he does not hinder their progress in getting her to control her powers.
People say that the line "Things always turning out the way you like is a precedent to unhappiness. There are things I can and cannot do. Recognizing that is key. There was an annoying person who said that long ago..." was actually from Lucas/Dawn battling Darach. However, I think that it was not the DP protagonist, but Darach who said this to her. If Darach was truly to look after her, then it would make perfect sense for him to be teaching her this. Furthermore, its strange for a silent-protagonist to suddenly be quoted. Even Red, who actually appeared in the sequel games, I don't think was ever quoted. Besides, this seems like a line one would tell a girl with uncontrollable psychic abilities as one is about to prohibit her from battle. As for being called annoying, its not as if Caitlin knew of Darach's feelings, and didn't seem that nice toward him in the battle castle. Besides, what else would someone who has Caitlin's power call someone who has none, yet stands in her way? I'm sure that, considering the way she says that line, that the word "annoying" is just being used teasingly.
So, tl;dr Caitlin has uncontrollable psychic powers, Darach taught her how to keep them in check.