You have a civil complaint, you have the option of filing a civil action in a civil court and sueing but I personally don't see that you would be succcessful . In order to win you have to be able to prove that they and something they did or did not do were at least the proximate cause of death.
Because the dog died so quickly, I would think the dog was seriously ill and probably might have died regardless, then you have to prove that you were damaged in some way, you could do that, the loss of your dog but the cause of death would have to be put squarely on them, very dificult.
You didn't say what the cause of death was, did they tell you? Just because a dog or a person has a tumor doesn't mean they will die. I have had three removed but they were not in a place that caused a problem and thankfully were not cancerous.
If it's not too late, see if you can find out exactly what the cause of death was, that might make your decision easier to make, if he had additional problems such as gaseous gangrene caused by the tumor there is nothing that would have saved him if internal organs were damaged beyond repair.
There are many things to consider and some information you need to gather before doing anything. I'm not a veterinarian or a lawyer, I just work in the legal field so don't take this as sound legal advice OK, but I would look into things a little more carefully before I jumped up and did something rash. Sorry about your dog, I've had one for 11 years now that I know won't be around much longer and my whole family thinks the world revolves around him.
There are also organizations found in the phone book such as th BBB and the state regulatory agencies you can make a report to if there is an indication of negligence.