I wouldn’t - cats don’t understand cages. IMO, befriend her, give her someplace safe and warm to have the kittens, and after they’re about 6-8 weeks old, trap, neuter, and release the family.
Also, call a local animal rescue group in your area and see if they have any suggestions. They might also be able to help with the TNR.
I’ve been trying but she always runs away. :(
I just realized that if I catch her and cage her, how do I clean the cage?