@Hobbie I dunno, it seems like it’s one of those things that shouldn’t be your problem but is.
I had a similar issue, when there was a horse here. Cats love horses. Sometimes cats try to move in. I haze them (shout personal remarks, jump up and down, throw things. This works better if it’s a coyote or a cougar, that hasn’t already learned that humans are largely okay and has somewhere better to go) and it’s semi-effective. But once somebody elses’ barn cat decided to have kittens in our barn. Sometimes they’ll take the kittens back to their own ‘home’ barn somewhere in the neighborhood, once the kittens are grown enough to make excursions. I kept hoping for this to happen, but noooo. The mother just dissapeared (those coyotes do that) and I had two feral kittens to deal with, and before I could catch them one got the sniffles and died. The horse gave every appearance of blaming us for it and was sulky and uncooperative for days, and I caught the surviving kitten and am the owner of a now-grown cat who can’t be rehomed because he’ll claw the crap out of you for no evident reason from time to time.
ETA: This is a lot less common than it used to be, and it’s all because the humane society will give you a desexed otherwise-unadoptable feral cat for free for a barn cat.