I doubt mama has a home or she would have been comfortable to hang around you and bring the kittens with her.
Since ferals aren't always skinny or scruffy and can look like well-fed house cats, she could easily be a feral that is finding food somewhere.
Have you seen her lately? Maybe the kittens are coming out because she's not around and they're getting hungry.

Now is the time to get your hands on the kittens and get them socialized. I'd start sitting in the area where they're emerging from the deck and would entice them with some canned cat foot or tuna. Let them learn you're not a bad thing!
Is your animal control a no-kill shelter? If not, you may want to start calling some rescue groups. Kittens are much easier for them to place in homes and they can give you advice on the best way to catch them.

Go ahead and use the trap. If you get a critter, just turn it loose. They're old enough to leave their mother, and will become tame pretty quickly at this age. If you put the trap out during the day with canned cat food in it, you're much less likely to get a skunk or coon. Will the shelter take the kittens? I don't think putting some shelter for them or food and water is encouraging them. They seem to be living there anyway. If you can trap the mama cat, maybe the shelter will spay her. She needs to be spayed!!!

Mama was under deck with kittens yesterday when I got home with 2 of the kittens... at least that's all I could see through the cracks. Last night's (and today's) weather isn not the best... rain... luckily not POURING. I put the lid to a spare litter box out on deck as a make-shift shelter... saw 3rd of 4 kittens walking inside before it got dark last night.

Another DUH moment! Set the trap during the DAY!! Raccoons, possums, SKUNKS... not around then!!

My township animal control guy stopped by and set up 2 traps. Both are covered so if it rains again, not a major issue. Said he'd stop by around 8-9 tomorrow morning to check and then again some time in the afternoon. Told him pretty sure ONE kitten wouldn't have enough weight to set the thing off, but if that can of food draws them all in... maybe mission accomplished?!?

Do you think the kittens are weaned then? If not, what happens if the kittens are caught and not the mother? It's a hard call as to what to do. Good luck. If rescued, hope kittens and mama fair well at the shelter and find good homes.

Mama is IN trap on deck... as of about a half hour ago. Sounded like a RHINO out there! But she settled down after 10 minutes or so. Animal guy assured me she might not be happy, but would be fine till he stops by tomorrow morning. Told me to do nothing if I see kittens out... looking for her?!? A total guess that kittens might be 4-5 weeks old?? They seem totally mobile and really fast... though I'm sure still pretty vulnerable.

So you can't find the momma or kittens now?

NO! Mama is in have-a-heart trap on deck. Animal guy said kittens might try to get to her. I don't know??

My guess is the kittens are still nursing since the mom is still coming and going. What did the animal control person say to do with the mom? Is it still raining, is she in a protected area, and is the trap partially covered?
Personally, I would slowly approach her just to see if she acts really wild of if she accepts your presence.
Did you ask him what they will do with the mom and kittens?

I hate the idea of her being caged so long, so check her now and then to make sure she doesn't injure herself.

If I were you, I would move the second trap so that it is alongside the first trap with no space between them. Adjust the covers to that they do not extend down between the traps (so that momcat can see and be seen from the other trap) but completely covers the tops of both traps. The kittens will likely enter the other trap during the night to try to get close to mom.

Took quick peek at mama this morning. She seems fine but is DEFINITELY NOT HAPPY!! Cat (and kittens, when caught) will go to county animal shelter. AC guy said he'd stop by to check around 8 this morning and do whatever needs to be done to lure out kittens... low side of deck is pretty much right on the ground and "high" side is too low for a person to crawl under. Will just have to wait and see!?!

That is a shame. The kittens can not nurse or eat since yesterday since mom is in the trap. The shelter will euthanize the mom and maybe the kittens too as they are probably overloaded with kittens this time of year and they need to be socialized and maybe weaned too. It is a shame the mother could not be spayed and released, and the kittens caught and socialized/fostereed and adopted. the mother cat must be really stressed both being in the trap and not being able to get to her nearby kittens.

I agree. The queen is undoubtedly extremely stressed not being able to get to her kittens, and she's also probably in pain with full teats. The kittens won't last long without food, warmth, and protection. I hope the animal control officer was able to successfully capture the kittens and remove them and the queen to a safe environment together.

Please give us an update ASAP.