Buying a single socket for the caravanning is not a bad idea, even if you have a comprehensive set IMO.
The van's 19mm could be the same size as your car's; but if not both are best carried in the car, it will therefore be readily to hand.[Many domestic cars though will have smaller hexagon sized bolts]
Be careful as if as assumed you have alloy caravan wheels, just confirm the particular 19mm socket acquired is not too big a diameter to fit inside any reassessing holes the wheel bolts are in. Here Clive's good advice to go for the inherently stronger hexagon type of socket is more likely to be suitable.
Clearly you have the obligations to meet you have undertaken.
However, it is the initial settling of the bolted wheel/hub assembly after
any refitting of wheels where the way greater risks arise, and this becomes more critical where alloy caravan wheels are used. There are complex differences with most European caravan wheel assemblies, as generally opposed to our cars that make attention even more critical.
I think towing 50 miles post a wheel refit prior to a quick check is too much, my recommendation is aim at the first viable stopping place after about 15 minutes towing. Very likely all will be fine, but it just might not be and towing that distance is likely to reveal any settlement before it has serious consequences.
Once, you have checked them on several outings they are very likely to be trouble free from then on, and I must admit it is not an every outing routine for me, more every couple of monthly as convenient.
There are some replacement wheel bolts that greatly minimise the underlying issues and one caravan maker adopted them as standard following their product having a high incidence of wheels coming loose. If ever they come loose then coming totally off is very soon going to follow as it is the clamping of the wheel to the hub that is key in automotive wheel bolting systems.
Bolts readily commercially available offering a real higher level of safety are WSL , these embody some critical differences to the standard bolting.
LINK . Other purchasing sources exist out there.
This is not to imply the standard bolts are not adequate, but as you have witnessed caravan dealers go to great lengths to stress the caravan's wheel bolting system needs "watching", not completely without historic cause.
It is just some of the safety factors can be improved on by using bolts with the features WSL employ in their product.