Problem

The trigger stimulus to the excitement state is clearly some action associated with the car and the excitement is made worse by the confinement and frustrated anticipation that getting in the car entails.

The excitement behaviour is unwittingly encouraged as the dogs behaviour apparently brings about a favourable result i.e. being calmed and patted by the beloved owner or by arriving at the eagerly anticipated place for a walk.

The motion of the car and sound of the engine may cause conflict and fear within the dog and this together with confinement and frustrated anticipation leads to an increase in excitement.

Treatment
The dog must be systematically de-sensitised to the trigger stimulus.  Praise and reward the dog as long as it remains calm.  Totally ignore the excitable behaviour.

Once the reward that initiates the excitable behaviour has been determined e.g. the journey to the park, watching passers-by, then the reward must be seen to be given only for calm behaviour e.g. on the way to the park only proceed when the dog is calm.

Small dogs may be benefit from being prevented from seeing out of the windows by being kept on the floor.