I have to agree with Denyce, although this is probably the worst thing for a kitty in this situation.....

If this kitty was your nieces, is there any chance of contacting her and asking her if she can take it in now? She might be upset to know that the poor kitty is going through this and her mother doesn't even care (sorry KYS).

Please let us know how this turns out, KYS. And thanks for stepping in and convincing your sister to take the kitty to the vet again - without putting her to sleep.