ha ha ha, trapped in a cat love, i see?
cats are definitely NOT beach animals. you can teach them to accompany you on trips out, ride in cars with no cage, go out for walks on a leash. if you decide to keep jemima and make her a dog-cat i suggest you give her time to recover, recuperate and perk up. maybe 2 more weeks so she is stronger, fatter and more sure that she will not be thrown away again. then teach her slowly and she may make a great animal to accompany you on short outings (although never as much as a dog).
i fully understand you... we took in a homeless pregnant cat. we were supposed to help her with the kittens and then release. the kittens are now gone and poor puryear slaves away as their human minion. and the mother... she's like "no, i'm good here, thanks for asking". she spends whole day napping and begging for treats. we did not want another cat. but we cannot just toss her out after the hell she's been through (she was very sick as two kittens were stuck dead inside, a surgery saved her life). and she is such a cool, loving and tender animal, who likes to be petted and in the mornings she is so overjoyed to see us it's almost comical.
so yeah, i know the feeling. on one hand you really do not need anymore trouble and on the other hand the little bastard has already stolen some hearts
my best advice is to keep working on her for now so she gains some weight and strength. ideal time to give away a kitten is at 2 months. it will be fully litter trained, eating dry food and capable of being on its own: going out in the garden, playing and so on. keep this thread going to soften hearts
post few pictures. this will also give you time to decide whether you want the kitty or not. and it will also give dr1ers time to ponder if they need a kitty who has beaten the odds
good luck yet again.