Some random thoughts:
1) I felt for Jenny, leaving all she was used to, her place of comfort. I can put myself in her position all too easily, but between the lines you can see Sally wanted to get her away from a place with creepy teachers, a charming but rather distant and irresponsible father, and friends who smoke weed. At the same time, Beagle acknowledges that any place has its dangers, although the dangers of Dorset may be somewhat idiosyncratic.
2) And Sally needed new opportunities. Beagle does a fine job of sketching in the relationship between Sally and Evan, of showing us through Jenny how well they fit together: “Sally came to stand beside him, and Evan put his arm around her. That made me feel funny – not so much him, but the way she flowed against him like water, which I’d never ever seen her do with anybody.” And there are other lines and passages that indicate how well they merge, show the partnership they’re forging – sometimes simultaneously indicating Jenny’s jealousy.
3) Why cats? Well, early on Mister Cat is the locus of good sense, or at least Mister Cat is where the older Jenny locates the more sensible reactions to what is happening. Young Jenny gets defensive, scared and argumentative, and Mister Cat sniffs and acts like it’s beneath her – and certainly beneath him – and she adjusts to live up to his higher expectations.
4) Why Jenny? Because of Mister Cat and, probably because of Julian. Tamsin choose Jenny from what she saw of her and that included the unconditional love of the cat for Jenny and how it was reciprocated, much like Tamsin and Miss Sophia Brown. It also included how Jenny, prickly and belligerent in so many situations, showed a good deal of patience with Julian, who is obviously in so many ways a nuisance, but also good-hearted; his adoption of her from the first is one of the most endearing things about the novel.
5) I can understand how the early part of the novel could seem the most engaging and Tamsin's story not as interesting, but I found the thought of a ghost only holding itself together through an effort of memory fascinating. Usually literary ghosts are a product of intense emotion. I've read quite a number of ghost stories and I can't recall a ghost whose composition was so reliant on its own memory. And that ties in with Jenny's impetus to write the book, which is to, essentially, honor and not forget her younger self, warts and all.
Most of Tamsin revolves around memory in one way or another: Jenny's growing pains from dealing with the memories of life in NYC contrasted to the very different life she finds around Dorset; the older Jenny's coming to grips with the sometimes frustrating, sometimes admirable young girl she was when she went through her adventure with Tamsin and, as Algernoninc pointed out, finding her way from the worlds intersecting in Dorset to the seemingly less abundant reality of Cambridge (and isn’t it interesting that a Pooka could be so instructive and insightful?);
Tamsin's efforts to remain somehow whole and coherent against a force dedicated to absorbing her and incorporating her within itself, and that effort mostly involved with remembering her life and her love; the Judge's memory of his love for Tamsin, no matter how twisted and skewed, and his memory of hatred for ... well, just about everyone.
(Toma, you quoted one of the paragraphs I marked in my copy of the novel; it's another instance of Beagle observing how people behave and finding pitch-perfect phrases to convey it.)
Interwoven with this is Jenny coming to appreciate something about her new surroundings: Tamsin and Meena are her entry into her new surroundings, finding what there is about Dorset that she can love and adopt as her own or adapt to. There is a wonder and abundance to this new world that makes Eighty-Third Street seem walled off and even provincial for all the big city around it. Jenny was on the cusp of growing up, teetering on the brink of a self-awareness that would lead to understanding others but hung up on that cusp, not moving forward. Without both the romantic and prosaic life of Tamsin to latch onto, her entry into empathy for others might have been much delayed or stunted.