Hey, Hissy, you are a right firecracker! Not that you are not saying what most of us also think.
The cat is 11 years old. It is clearly one that has a territorial bond rather than a bond with its human caretakers, because 11 years is time enough for the cat to love its human more than any territory, and it clearly doesn't. Moving with cats that are strongly bonded with their humans is not really that difficult. A few weeks in the house, regular feeding times in the house (and not outside), and a lot of special attention for a while during their "getting acquainted with the neighborhood" period is usually enough. I had two cats for only a year in California -- both strays off the street. When I was getting ready to move, I was beginning to take my things across Berkeley to a new apartment and the cats jumped into the car and sat on top of the first load, and all the loads thereafter until the old house was empty. The cats got into the car through an open window on the last day before I had even started to look for them to take them to the new place, and they settled in immediately and with only a little shyness. I was too stupid to understand the compliment they were paying to me and to our relationship. That was back in the days when cats were considered to be much less intelligent than dogs, even by the experts. I know better than that, now, as well.
But lots of cats don't really bond with their humans. Perhaps the chemistry is not good, or the cat or the humans have cold or impersonal temperaments. These cats can be happy with just about anyone who feeds them and gives them kind words and shelter -- just so long as that person does it in their territory, to which they are fiercely attached. I have several strays who love the neighborhood, and like me well enough, but if the neighbors are having a party, they'd really rather eat there -- or down the street two houses. They come (to my) home when they are hungry or thirsty, stay for a little socializing and petting, and then find a nice place to sleep in a vacant house across the street. They know they are always welcome, and that's enough for these free souls.
It is a little ego-busting to learn that your cat prefers eat at a neighbor's or to stick with the old neighborhood, even though this is a far more embedded instinct than bonding with an animal of another species (human) and abandoning all the familiar places.
Cats of this type will NOT adjust to a new neighborhood where they don't feel comfortable. They would rather become feral and die in a ditch of dog bites.
Try to make your brother and sister-in-law -- (or are they split? which could also provide a partial answer to the cat's rejection of being transplanted) -- understand that the cat is a territorial cat rather than a people cat (don't mention that the cat may well bond strongly to someone of a different personality or chemistry). That you would love to let the cat stay with you, if that is what the cat wants. Be very low-key about your wanting the cat. You are just willing to be helpful in a situation that is essentially causing great stress for the cat. Take him to the vet and get him checked over. Then tell your sister-in-law what the vet says about his health, his condition, and any words of wisdom about cats that are often unable to make the move to another territory successfully. Don't say at all that the cat plain is not bonded to her. Bad psychology. Stress the naturalness of the cat's behavior. Stress any comments the vet may make about his condition (anything negative is helpful, even if exaggerated a little). Your sister-in-law needs to feel that she is not deficient or being criticized, or she will cut up stiff.
Offer to look out for a similar kind of kitten for her -- or a friendly puppy (dogs are less discimminating about their humans).
But get your way firmly, because this cat will probably end up dead someday trying to get back to the old neighborhood. Definitely feed the cat. Definitely begin to take it indoors for a few hours at a time so your cats will accept it. There is an ancient right that all cats demand -- the right to choose their poisons -- which humans, which territories, even which deaths (related to their other two choices).