I'm pretty sure that the reason Kris keeps going to the swimming pool is that it is supposed represent Walden Pond. Walden was the book she read. Stones are key feature of Walden Pond mentioned by Thoreau. They mysteriously surround the real pond. Kris keeps diving to find stones and them around the edge of the swimming pool. Thoreau relates a story that the pond was the scene of an ancient Indian ritual that angered the gods, who sent the stones rolling down the mountain after them. Now how stones got on the bottom of an indoor swimming pool? Who knows.
Diving to the bottom of the pool was a metaphor. She was diving deep into her subconscious and finding the memories she had when she was drugged. When she went into her subconscious she was also rehashing Walden which was a menial task to keep her busy while she was drugged.
At the surface level (pun intended), being immersed in water helps triggers repressed memories of the brainwashing experience. Kris discovers this in the bathtub; it's the scene immediately before the first pool scene with the stones. And this relates to the fact that a newly-swallowed worm needs to be kept immersed in water to maximize it's mind-controlling powers (hence the constant water drinking at carefully controlled time intervals).
We see Jeff dump stones into the pool before Kris retrieves them all, as they gather the set of quotes that they use to identify Walden as the book used during the brainwashing. This implies that in all but the first such instance, Kris put them there herself.
Now, there are several possibilities for the first time:
1) She got lucky; there were stones already in the pool, and she removed them to be a good citizen, and as she did she had a fragment of Walden come back to her.
2) She somehow figured out beforehand, or had a strong intuition, that retrieving stones from the bottom of the pool would be the best way of triggering memories.
3) Since both of these seem somewhat unlikely, the best guess may be a hybrid. Her bath experience leads her to try immersing herself in the pool. She happens to find some object in the pool and she rescues it. She gets a flash of phraseology from an unknown source. And it's a passage where the stones are mentioned. So she gets some stones and tries those, and they work great.
Now I have to watch the film an 8th time to see if that theory works!
Prepare your minds for a new scale of physical, scientific values, gentlemen.
I took it that it was the after effect of the mind control, unusual habits/direction. But, there was the repressed/hidden memories of it. She was unknowingly tapping into her former worm-induced learning. Also, there was the connection to the water-loving former host. So, just as she experienced pain, love, and frustration/imprisoned feelings; I believe that the pig also expressed somewhat human/universal feelings that she felt. Pigs love Walden Pond perhaps, there's definitely a hidden influence she doesn't grasp until late in the film, when she responds more directly to her linked animal. A universal need for love, understanding, and parenting. And also, that baby pigs are cute and cuddly.