I'm so sorry.
Pets don't really have rights. In the US they are considered property. So any type of legal action may not get you far.
Sometimes this just happens. I know some very good vets that have lost patients. All you cam do is take precautions before surgery (preop bloodwork, maybe an ekg, use only the best anesthesias, etc.). If you were not offered bloodwork or if an IV was not placed or if a cheap anesthetic was used or if your pup was not kept warm then you may have some ground to stand on. However, I am guessing you had to sign a consent form agreeing to the procedure which would be binding unless perhaps there was clear wrongdoing.