No, no, no, OP, do NOT explain exactly what happened. Especially given the bit that you couldn't afford to fix the dog's leg and went with the cheaper option of euthanasia. Even more so with complaints about "threats of sexual violence, expressions of a desire to rape, requesting sexual favors, attempts to damage interpersonal relationships of others for personal gain, boasts of illegal sexual deviancy, and I promise you, this list doesn't stop there" floating out there. You really don't want to get in to a five minute discussion about your animal husbandry.
"She's making it sound worse than it was. I was playing with the dog and it accidentally got injured. The vet's recommendation was to put it to sleep. Obviously, I feel horrible about it."
Then shut up, you've explained yourself fully. Don't give them the opening to ask for more information. If they do push for more information, just say, "I feel horrible about the accident and would prefer not to talk about it." and then go all Iago ("From this time forth I never will speak word.") on them. It's a horrible memory (even if it's not all that horrible to you, pretend that it is,) and you have a right to not have to re-live it.
And while I'm on the topic, if someone brings up your fetishes in a negative light, adapt that phrase to address their concerns. "Look, that was meant to be private, it's something that I only do with fully consenting and willing partners in our own private bedroom."