Thanks for the additional information. It is helpful.
I suspect that she has injured a disc in her back. Dogs who have a disc injury often avoid stairs and jumping. Trembling is a sign of pain and when in pain many dogs want to be as close to their owners as possible. In a car, there are unexpected body movements that a dog can not control and thus she might have pain unexpectedly adding stress to the car rides. Stress can also cause trembling and different behavior. She may have injured her back when the other dogs was there as it does sometimes take a short while for the injury to be evident.
An intervertebral disc that has slipped or ruptured up into the spinal canal causes inflammation of the spinal cord, which in severe cases causes paralyses of the rear legs. in less severe cases, you see dogs avoid things that might cause them pain such as jumping and stairs. You can read about this here:
Large dog breeds sometimes suffer from a condition called degenerative myelopathy which can also cause problems with the rear legs and paralyses. You can read about this here:
Buffered aspirin can be given to a dog with a dosage of up to 5-10 mg per pound every 12 hours. Keep in mind that a dog's body does not metabolize aspirin in the same way as a human and thus should not be given more than a day or two without contacting your Vet. The aspirin may need to clear your dog’s system before other medications can be given, so keep that in mind if you decide to give aspirin and be sure and tell your vet when your dog is seen. Read side effects and precautions here.
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Since there have been recalls on certain foods, please check the following site to be sure the food your animals eat is not affected. If it is affected, contact your vet as soon as possible. Have your dog seen if they have any symptoms.