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.
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.