Mostly, new kittens eat and sleep. They cry if they lose a nipple, though.
You can't be sure about the joint parenting. This was a program about a group of barn cats who were always together. I would definitely get a bottle and kitten milk from the vet!
When you want to trap, it's best to camouflage the trap as well as you can, and skip a meal or two, if at all possible. (I'm thinking of the nursing mother, who needs more to eat than usual.) Some people skip an entire day. Perhaps you could close the garage with food inside for the new mother.
Move the traps to a different location, camouflage, and hide and watch. I hope all is well with the kittens. One thing you have to be careful about is feral males. They often kill kittens.
As for the cat I had with the C Section, that was my experience, and the vet approved. Of course, if your vet tells you not to spay her, don't do it. I don't consider myself an expert. I have learned from experience, reading, and watching educational videos.