I am very sorry to hear about your dogs. I think most anti-coagulant poisons are banned now.Rat poison is definitely more torture. I had two dogs that got into some when our barn girl was stupid and put it out. It takes days for them to die and their lungs eventually fill with blood. They drown gasping for air. They had to tap our dogs lungs several times to stop the, from dying and do multiple transfusions. They saved them but the vets were truly heroic. I wouldn't suggest it as a painless or quick method to kill an animal. Dumping it in water takes 1 minute and it's over. Shooting would be fastest.
I agree that poison should be an absolute last resort. I don't and will never believe that drowning is better than much, it's legally considered a form of torture.
If it gets to the last resort, which it has done for me once over the years (colony digging tunnels under the barn) I asked the local state wildlife ranger what would be safe to use, and what he recommended was really fast, they nearly all died underground in less than 2 days (not each, I mean the colony was gone). I can try to dig up the name if the OP needs a nuclear option.