I have a ferral cat. She comes from a region in Ontario where there are apparently thousands prompting a documentary on them.
Friends 'caught' her, although she seemed to be pretty willing as they were feeding her regularly. I know they just picked her up rather than trapping her. (she had already grown to trust them) They took her to the Hum Soc and she was spayed there. They then brought her to me. She purred so loudly the first night I had her with me, having never been in a home before, obviously thrilled that she was one of the lucky ones, that she started coughing seriously and had to stop. She never purred again until 5 years ago. I suspect it was the tube that had been down her throat that caused the coughing. I was stunned at how well-behaved she has been over the past 12 years. She truly is a sweetheart. She doesn't scratch anything she is not supposed to, never asks for food, just sits by her bowl quietly looking at me. She will eat ONLY cat food. She has to read the label first, just to be sure. It is strange that she will eat nothing else, no cheese, no milk, nothing. She did not speak until recently when I gave her appetite pills; she was not eating. I didn't even know she had a voice. Now I call them meow medicine. But she still doesn't say much.
She lived on a rural highway and apparently saw a lot of her little friends killed on the side of the road. She still, always, runs in when she hears a motorcycle, even though she is not in danger on a balcony.
All of that was about my experience with a truly feral cat and how contrary it is to what others are telling you. I have heard stories hear about shelters not allowing cats to go to homes unless there is a contract to provide them with very specific foods (some of which may not agree with vets' recommendations) and unless balconies are enclosed. I don't know how people get these regulations in their heads when pets are dying for a companion.
As for trapping, I guess you will feel bad about doing it but it must be done. She will be returned to her kittens? or not? You simply must do it. I can't imagine a wild cat needing fussy food. They must all be hungry so why wouldn't some cat food work?
Sorry I don't have help on the trapping. But I thank you for looking after the family. I don't get the bit about the kittens being unadoptable and untrainable. You put a litter box out for them in the kennel and they learn in a hurry.
Also sorry about all that other nonsense. Good thing the burst was not in an upstairs bedroom.
Good luck with the kids.
And thank you Paul, for saving replies that have not been posted, as I lost this one temporarily, right at the end.