Honestly, sometimes the best thing is realizing you're not the best home for that animal in that given moment. I've known several people who have adopted animals with extreme separation issues (that weren't really documented prior to adoption) and while they wanted to work with them and give them a good home, they realized their current living situation wouldn't allow it. It 100% sucks but you have to do right by the animal and this at least gives them the chance to find a place that works. None of us want to give an animal back to the shelter but sometimes the fit isn't right in that moment.
We spent 6 months on a Great Pyranees. We were told she was crate trained, house broken and great with horses.
She had severe separation anxiety. She tore her claws and gums chewing her way out of her kennel when we left her alone during the day. We trained her to be fine in it while we were home, but no amount of treats or toys could keep her in when we weren't there. We gave up eventually and tried leaving her in the livingroom. She destroyed the house. We started locking her in the kitchen with all food, dishes, everything cleared away.
She was food aggressive. We trained her to let us touch her and her food and actually enjoy it. She never did bite, but she threatened to with the kids. She say them as unable to say no.
She chased and barked at the horses. We taught her not to, but again, only when we were watching.
She loved dogs, but tried to kill and eat my goats and chickens. I tried to teach her that they were friends and she stopped barking when she tried to kill them.
On leash she was perfect. Off leash or out of the yard, she bolted every time. She hated going for walks and runs with us. She played fetch, but got bored after a few throws.
Eventually, we had a dog that was only happy on the couch with us or at the dog park. She was the perfect old family dog. Worst farm dog ever. We gave up after she started lunging for the baby goats when we looked away and couldn't be trusted not to knock over the kids to steal their food even with us in the room.
We brought her back to the rescue. It broke my heart. I felt like a failure. But, I was able to show all the work we had put into her. All the tricks she could do. Her immaculate grooming and willingness to put up with an hour of brushing every day. Her hugs. Her kisses. We described the perfect family: city family, kids over 10 and able to say no firmly, short walks and either dog park or obedience work rather than a jogger, tall fenced yard and hopefully a second dog. Cats were ok if they were dog savy. I had broke her habit of trying to kill the cats at least, even though we were told she was great with cats when we got her.
Sometimes we aren't the right family. No matter how hard we try. I did everything I could. I made her better for the next family. Twelve year old boy and sibling, city family with a lab that needed energy burned. She is happy. We still need another dog, but we learned our lesson on pushing it and are waiting for the next one to show up and ask to come home.