I feel for you. I know our local Humane League has a reduced spay & neuter clinic every Friday. I know you said your Dad lives out in the middle of nowhere, but is there a Humane League/Shelter somewhere in his area? If so, maybe you could check with them to see if they have something like that. The only thing is, you'd have to catch them and crate them to take them there.
Poor kitty. She's had so many litters of kittens that her body is not able to bounce back from all the nursing that she's doing.
Good Luck and let us know what happens.
