By Law, does a fl. vet clinic have to euthanize a dog if you ask them to?

Our dog is miserable and every vet clinic is asking to get a consult and an exam, and the dog is just the the end of her road. She's lived her good long life. She cant get up the stairs, and shes getting snappy, at out cats. We have a 10 month old and are worried she might snap at him too.