You can still have pity for the OP and the situation and still feel she made pretty bad decisions that contributed to the situation at hand. Yes the situation is horrible and I feel bad a beloved family pet has been put down but it didn't have to be this way.
Not licensing the dog, not have up to date shots, not having the dog neutered, not having a secure fenced in area if there was even a chance of the dog escaping. All of those are examples of irresponsible pet ownership
the neighbors had thier dog loose running around it ran over to our yard paced our fence till one of dogs got out they dug a hole my dog grabs hold of their dog wont let go neighbor is outside screaming in our yard me and dd run out to see whats going on
Based on the OP I am assuming the neighbor's dog was pacing the fence and barking. Her dog being unneutered and therefore extra prone to territory defensiveness got out of the fenced in yard and attacked the dog for reasons that are totally within his nature to do.
Now I have 2 dogs that are champion escape artists. One of mine is a territory protector. I spent lots of money making my yard escape proof simply because I do not want them hurt or injure anyone else. My dogs are not outside unless they can be monitored - I watch them through various windows or one of us is outside with them.
My next door neighbor and the people behind me have dogs and those dogs do pace the fence on occasion. Unless you are deaf there is no way you can not hear the barking and that you don't have enough time to bring the dogs in the house to avoid one of them getting out.
I think the OP made some very poor irresponsible choices. I'm saying this matter of factly, not to berate her. I'm not kicking her when she's down, but I can't help but point things out of hopes something like this won't happen again or to someone else here reading this thread.
I think she panicked and did what she thought was best before talking to behaviorists. The tasting blood thing is a wives tale- you don't attack another dog and turn into Cujo. Honestly what's done is done. I hope there is a huge lesson learned in this situation and all dogs in the house will be neutered, brought up to date on shots, and the OP will not put her dogs out unless they can be monitored and fence repairs made.
If anything I hope this is a lesson to people here the importance of responsible pet ownership. That includes awareness of the breed, obedience lessons, controlling the animal, keeping it up to date, and neutering them!