That's unreal OP.
Can you contact the council and report vermin (or some such) that you think is coming from your neighbours house due to the clutter and debris that is being 'stored' on their two-car driveway. Also, while in conversation, mention that carers are using your driveway without your permission, have been doing so for the past number of years and you want them advised that they are no longer allowed to park in your driveway.
Get the council and local health authority to deal with it.
Oh, and get a chain or bollards or some sort of device that prohibits cars from entering your driveway.
Can you fit gates? Would that be an option?