Welcome to Just Answer, I am so sorry you are having to deal with this. These are one of those situations where grief has overshadowed sensibility. I am assuming she was close to the dog.....and thus is trying to find a way to make sense of this tragedy. Unfortunately this is not the way to do so and in the end is affecting your relationship.
Sometimes women, tend to forget that us guys are not the fixers of everything. Women tend to sometimes rationalize that the man can fix and make everything better and when we are unable to they sometimes push the blame off on us without thinking it though.
The solution is to find a common ground with her and sit down and let her know how you feel. Let her know how this has effected you and how much worse it is because not only do you feel awful about it but you are also shouldering the blame on your own. Let her know how sorry you are that this happened but in the end, you can not be blamed for something that someone else choose to do.
Let her know how you feel........now is not the time to be macho lol. Let it flow, let her know how this is effecting you and your relationship and how you really want to get passed this. Explain that while blame may make her feel better, it isn't helping to straighten your relationship with her and is in fact causing a rift in the relationship. Let her know you love her and do not want this wall between you two.
Let her talk, encourage her to tell you how she feels about the death of the dog and ask her if there is something you both can do in memory of the dog. Such as a contribution to the local dog shelter in your dogs name or maybe consider adopting a dog from local kill shelter in your dogs memory to save the dogs life. Often this can be very therapeutic for someone who has lost a dog to save another one.
Consider having a small memorial built if she would like this to remember the dog and what happiness he brought you both. remind her that your dog was a part of the family and would not want to see his family ripped apart over a mistake someone else made.
In the end this will take some time for her to accept.....but if you remind her how much you love her and are sorry for the mistake this other person made hopefully she will get over this and come to terms with the fact this was a simple accident that had nothing to do with you.
I am not jumping in on your territory;however, while reading through posts this afternoon, I came across this post and because of my love for fur babies I was compelled to read it. There was also a comment that you made that I found very interesting and important: In fact, it is nearly a duplicate of what I shared with a customer this morning.
I would like to share with this customer: Walter is so right when he tells you that many women view men as being the fixers. I engaged with a woman and the comment that I shared with her was this:
One of the things that I find so amazing in society today is that in the short span of 20 years we have grown exponentially, and in many areas: Computer science, technology as a whole, medical science (totally mind blowing), the arts (one of my fav's because now I can see Andy Griffith in color...before you jump to conclusions I didn't get to see him in black and white. I was informed!) ...and the list could on...
And even more amazing than all the growth that society has made, the majority of women and even men (that teach the psychological sciences) are still in denial to the fact that just like woman, the man also has needs: The need to laugh, the need to love, the need to cry and be comforted, the need to be heard, and the need to feel good about who they are and most importantly from the one that they love for this is what gives the man the strength that the woman relies on...
You've received wonderful suggestions from Walter and as I said earlier, I am not here to but in. I would like to add one more thought and that is this...
When you are talking with her let her know that you are feeling hurt (Walter is right ...macho go for now...) because you loved the pup too. Then reassure her that you do realize how painful this has been for her ... continue by letting her know that as a couple this has become a problem. Let her know that once upon a time someone told you (by the name of Walter, LOL) that every problem has but two parts and as an individual it is up to us to decide if we want to remain attached to Part 1: The problem itself or if we want to take on Part 2: which is a solution to the problem itself. Let her know that blame only contributes the problem and then go to the shelter and bring home a few (I forgot I'm not talking to myself LOL) one that the two of you have chosen...
Good Luck... Never forget...You are important too!