Best buddies

On February 10 I posted a photo of a cat that had taken up residence in our barn. At the time I had no idea if it was male or female. It was what I would describe as feral- never let me get closer than 5 or 6 feet. On May 3 Mr M found her in the barn with a litter of 5 kittens. I was able to find homes for 3 of them. These 2 are now living with us, which brings our total to 5. The mommy is still basically living in the barn. I was in touch with the local animal sanctuary which said if trap her and bring her in they would spay her. We tried very diligently but have not had any luck. I watched her go in the trap to get the food and she stepped right over the metal plate that trips the door. Now she’s had another litter of 6.And at first they were in the barn but now she’s hidden them somewhere else but she still comes around to get fed. I’m struggling to figure out what to do.