David, whilst you may like the idea of leaving the hitch lock on whilst towing, I can assure you that the Emergency Services do NOT.
In the event of a situation where they need to separate your car from the van, the last thing they need to be trying to find is the key to unlock it.
In the complete history of caravans, NONE have ever been stolen whilst being towed at up to 60 mph , or more.
If you stop en route it is a 30 second job to fit it, or remove it before setting off again.
Also, if you stop en route, NEVER leave the car and van unattended.
You know full well that vans get stolen from service areas, you have all the needs you want in the van, toilet, cooker, fridge, kettle.
Eat your own prepared food and drinks which will be far more appetising than the stuff the service areas jokingly call food, and safer.