The Number is Three
There are definitely three cats here. One larger light gray tabby and two kittens, one dark and one a light gray.
I have honestly not had a close-up look at the kittens. The larger cat is now responding to me when I put the food out in the morning. She--I suspect she may be the mother cat--talks to me and stays out in the open while I am there although she is still very cautious about approaching.
At this rate, in a couple weeks I will probably be able to touch her. I am hoping the lure of food and my quiet presence will reassure her.
The kittens may be another story, but if indeed the larger cat is their mother, then they too will eventually come around.
All three were out in the yard quite a ways away from the barn when I went out. All three took off and dashed under the floor of the feed room--their "cave." But, as I said, the larger cat emerged as soon as I called and then, after a brief conversation with me, watched me put the food out and then waited until I went into the barn to feed the Boys before eating.
The kittens are much more elusive. They were nestled on the fuzzy blanket I put over the horse blankets at the end of the barn aisle last night, while the adult cat sat on the barn floor. Again, she did not run immediately, but the kittens slipped into the shadows behind the trunk.
Patience must reign. If I can catch the mother I will get her spayed ASAP. I can set the trap for the kittens and might be able to get them too. I have a fair sized wire crate I can put in the sunroom for a while to socialize the little guys before I take them to get neutered as well.
As much as I would like to, I simply can't add any more cats to the indoor "herd" so these guys would need to become barn kitties. If so, I will make some nice comfy, warm quarters for them. There are two garages, a carport where I store my hay, and the barn itself where they can always find shelter, but I special shelter for them would be even better.
Meantime, as long as the weather holds, they will be just fine as they are. All they need now is to learn to trust me.