Caught mom cat having trouble catching kitten

About a month ago a stray cat kept showing up on my property near my compost.  It appeared to be eating out of the compost.  I started to feed it, and move its bowl closer and closer to the house in preparation of catching the cat to take it to the vet.  One day that cat let me see that there was a kitten.  Before this I thought the cat was a kitten itself, so now I felt it was a rush to catch the cats.  I caught the mom  2 days ago and have had her spayed.  But the kitten I have not seen since I caught the mom.  The kitten never would come to eat from the bowl ever.  Only the mom would eat the cat food.  The kitten only showed herself when the mother was there.  While trying to catch the kitten I have attracted a huge skunk and caught a racoon.  But no kitten.  My mom thinks I should put the mom cat in a carrier outside and try to use her to lure the kitten to the cage.  I am hoping the kitten is old enough to be on its own. It is the size of my hand and is very active and jumps around playing when the mother was around.  Any suggestions??  I feel awful, because I feel the kitten may have not survived because I took the mom away to soon.  I also don't know if I should just release the mom to help the kitten.  Technically I could release her tomorrow, but it is the best for her health if I hold onto her for 10 days till she is more healed.  I still have not decided if we are going to have her live in our house or rerelease her to the wild.  But I would release her to the wild if that is what is best for the kitten.  She still has not peeed or pooped and is not eating well, so I am not encouraged to release her yet.  Any one have luck catching the baby after catching the mom?

You can try that method but it may make mom cat more nervous, being outside and trapped in the carrier.  It may stress her more than she needs right now, as she is still recuperating.

Is there a way you can do an organized search for the kitten?  Have some friends work in a grid and walk through the area.  Look under bushes, debris, wood piles, sheds, whatever he or she may be hiding under.  I wouldn't have anyone grab her yet but this will let you know where you need to set the trap.

I once trapped a mom cat, not knowing she had five week old kittens.  She was on my porch, recuperating for almost four days when I heard the kittens in the brush where I'd trapped her.  I put up a crate, put a plate of food inside and tied a length of rope to the door, looping the rope through the top of the crate and walking a distance away with the other end of the rope.

Within five minutes, the kittens were in the crate and I was able to pull the rope and close the door.  They never even noticed!  This method might work but it sounds like you will have to have a lot of patience.

Thank you for helping mom.  If at all possible, I would keep her inside as long as necessary (and forever, if she adjusts to being inside).

I think you shall try and combine both chances, both of your own suggestions.   Have the mom in a nice carrier, as bait for the kitten.  You will at least see if the kitten is still alive.

If possible, have a trap prepared.

I presume you have food out for the kitten?   IF?

Second, if the kitten doesnt show itself  be prepared to release the mom.  Not optimal, but  stray cats are tough survivors.  If they arent tough survivor, they do perish before they come so far...

I understand you are willing to try and foster this mom cat?   Sorrowfully,  I suspect its more urgent to try and save this kitten.  Even if the mom becomes trap savvy, and becomes more difficult to catch again.

Good luck!   @Seaker

ps.  I see  the wise Ondine who answered simultaneously, has partly different advices.

You being there must decide yourself - YOU are the pilot on this flight...