I've got an elderly cat that became my responsibility through... circumstances.
He's a lot of work. He has zero personality or charisma. Worst of all, he harasses me for wet food his whole waking existence. Food motivated is not the word, it's the only thing he knows, or cares about.
Your family gave that dog a second chance at life for a long time. Someone just permanently damaged him before you guys met each other. Even if he never became a friend, you still gave him more moments of comfort and safety than he would have seen had you guys not taken him in. It's sad he couldn't recover, but if giving him up was the end of his story, you still gave him all you could before that.
Working in animal rescue, I think a lot about animals that can't be saved, and sometimes a calm and peaceful end isn't the worst outcome. You probably know all this, as your story makes you seem very compassionate, but just in case, you shouldn't feel guilty. You guys went above and beyond what most would have done for that poor dog. ❤️