You have my sympathies. My cat never adjusted to us bringing our son home. She hated him. He was only a newborn, barely cried, never touched her, she just hissed and walked out of the house and we literally never really managed to coax her back. She was permanently anxious. As he grew he would stroke her gently, which she didn't mind, but she would constantly leave the room he entered, as if she was startled, and run outside. She made a home in the shed and preferred it there.
I had no idea what to do. Rehoming her was unthinkable, but all manners of gentleness, treats and kindess wouldn't get her to share her home with kids. Maybe it was a memory of her previous home (she was a rescue cat) or something. She would come in, eat, drink, and leave again.
Bizarrely she liked my second child more. She began to follow her around, rub against her, slowly began to stay in her cat bed a little more. But after a few months of slow improvement, she grew sick (pre-existing condition) and she died.
Point being, I still feel so guilty about her final years. I refused to consider rehoming her - I loved her! - but logically I had to accept she was no longer happy in our home and we could not give her what she needed (probably a child-free home.) Or perhaps there was more I could have done? One more trick that may have coaxed her in, one more Pinterest-inspired tale. I read about high-up cat beds on pillars, where they could keep watch; now I regret not having one. I read about letting them live upstairs with the children downstairs - should I have done that? Regret and guilt all over again.
Basically... I don't know. It's really hard, because you think of rehoming as something irresponsible, something 'throwaway', and yet there are times like this when it isn't so clear cut.
If the cats don't like a new home with you they'll hate one anywhere else, so maybe that's the first reason to put it on the backburner. There's a good chance, as said above, they're being fed elsewhere. I don't know if 'love bombing' cats is appropriate - keeping them in for a week, loads of affection...? Cat might hate it. Probably will. Not sure.
Maybe there are other cats in the garden leaving their own scents and pissing your cats off?
You could also consider some kind of outside house for them, so if they're going to be out there they've got somewhere dry to be. It's not ideal, but if it's what they want.
It's a tough one. I wish I had the answers.