Typically family groups are looking for vacation houses which are located not directly in a city but more on the landside or at the coastline. Of cause these houses have a kitchen and everything that you need. Typically the families then do day trips to cities or beaches. In the evening you cook or do a BBQ together and play games until kids to to bed.
Wimdu or Airbnb are wrong tools for that.
This article from VisitDenmark provides more information about that vacation model and names the relevant online platforms that are also used by most of German people for example.
Regions: Personally I like North Jutland's North Sea shore which feels rough and windy; sometimes also rainy. It is allowed to drive with the car onto the beaches. So at a sunny day you drive on and look for your private dune to stay for a while. From North Jutland you can do day trips to the city of Aarhus (2nd largest) and to Billund's Legoland (for the kids).
Danish Riviera is comparable mild and a beloved area for smaller private sailing yachts. Closer to Copenhagen is the shore around Helsingør. Far away is Bornholm island but I like to mention it because it is known for its fantastic reputation as vacation island for all ages with a lot of sun. I spent 10 days there in 2021 - planned were six.
