Hi Debby, sorry to hear about your problem with your dog.
Firstly, you can't be sure your dog has no health problems, you can only be sure she has no
diagnosed health problems. My dog would often refuse to do things and it was only a long time later (after transferring to a new vet) that I understood that he was in pain. The only difference this makes in your case is to confirm that trying to force your dog into the car is a bad idea. But also to be aware that until we find the real cause we can't absolutely know that a particular puzzling behaviour is not caused by health issues.
Secondly I would start by shaping your dog to
- approach the car
- approach the car with the car door open
- put a paw in the car, Take paw out of the car
- put front paws in the car, take paws out of the car
- Step further into the car, get out of the car
- get in the car, get out of the car
- get in the car, close door and instantly open door, get out of the car
- get in the car, you get in the car, you both get out the car
- you both get in the car and sit in the car then get out
- both get in, you start the engine you turn the engine off you both get out of the car.
Make a game of it and repeat each one of these stages (and break them into smaller stages if necessary) until your dog is really happy to get into the car for the reward before moving onto the next stage - so don't ask your dog to out a paw into the car until it is approaching the car enthusiastically. There are a number of benefits to this approach
- If you take the time to get your dog absolutely secure with each stage of the "game" there is a good chance that you will come to understand what is triggering your dog's behaviour because you will see when she is unwilling to progress to the next stage.
- If you figure out the stage which you dog finds difficult you can work on this part of the game and make it extra fun where ever you are when ever you are getting into the car.
- Even if you never figure out what the problem/trigger is by making a game of getting in and out of the car you are counter conditioning/desensitizing your dog to the trigger/negative association.
- If your dog won't get into the car you can start to play the game - it might be possible to quickly work through the stages and get your dog into the car.
Hope this helps

Please let us know how you get on and feel free to ask if I haven't made something clear enough.