Your daughter is being far more charitable than I would be in her place. What you did was not only terrible, but also illegal. The cat did not belong to you, you did not have the legal right to have it euthanized. You stole a member of her family while you were a guest in her home and had it killed.
Your daughter is and was an ADULT. While certainly you could have expressed concern about her finances, that is the end of what was appropriate for you to do here. It was her decision to make, not yours. She likely viewed the cat as a family member, and you killed her family member. If you were my mother and had taken and killed my pet, I'd never speak to you again, and I'd likely have involved the law over it; but my mother would never have done such a thing.
When my oldest dog was a puppy, and I was about your daughter's age, he shattered his leg and needed expensive surgery to fix it. My mother expressed that it was a lot of money I didn't have at the time and thought I should have him euthanized. I had the surgery done. Yes, I went into debt. And then I made a budget and paid it off. It was not the end of the world.
Add: NONE of you have any idea what was in the cat's best interest. All we were told is the cat was sick and surgery wasn't "guaranteed" to fix the problem. Nothing is EVER "guaranteed" to fix ANY problem. For all you all know, the vet could have said there was a 95% chance the surgery would fix the problem. This decision should have been solely between the pet owner and their veterinarian. I treated one of my dogs for an illness two years ago. They gave him a 5% chance of survival. He pulled through and was back to normal in a few months. It is not cruel to treat an animal for medical problems.
This asker STOLE their independent adult daughter's property while visiting her, and had her companion killed rather than rationally discussing their concerns with her.