i agree to be honest - suing them will be both expensive and probably ultimately futile. As long as you are not out of pocket, i can't really see what you would be suing for: would money make you feel any better that your dog died?
If you didn't know till you came back, i doubt you could claim you had loss of enjoyment of your holiday. There was no malign intent behind it on behalf of the kennels, and if your dog was so ill or old that having a relatively simple op made him nearly die, you couldn't really prove that his ultimate death was down to their negligence. Dogs meet other dogs when they are out for a walk, and it could quite easily have happened anywhere - i don't think you could say it was their "fault"
Im sorry that such an awful thing happened, and i would be very angry if it were me, but i really think you will just cause yourself more hassle