I You plan on attending and are going by public transportation, I would suggest that you mention it here. It may be possible to arrange pickup from the station. It is a fairly long walk from the closest busstop and they are not going to often in the weekends.
Every vehicle in those photos (including the Land Rovers) was also in service for the Australian Army… Although we put a Scorpion turret on our 113’s:
There would be no issues for you and your son as it is a public event. It is open from 09:00 to 16:00.
CPH Copenhagen Airport is the only possibility.
Unless you rent a car you will be dependant upon public rail transportation to get to Næstved from the airport and then a taxi to Skyttemarksvej 192 4700 Næstved where the event is happening. The taxi from the station to the event will be about 26 euro alone. A oneway ticket with the train for both of you would be about 23 euro.
Knowing how you feel about trains it would probably be best to rent a car.
According to carjet.com it is possible to rent a car at CPH airport for 2 days from 13,43 euro and up.
I don’t know about any hotels or any other resting places nearby. But PM will be sent.