Hi, Please bring your senior dog to the vet for bloodwork. The
symptoms you have mentioned, along with the dogs age, remind me of the same thing that my 15 year old yorkie was doing. She was diagnosed with kidney disease. Decreased appetite and trembling are both signs of kidney failure.
Your dog may or may not have kidney issues, but the trembling, (shaking) you are describing, is a sign of pain or discomfort. Your dog really needs to be evaluated by a vet.