If you're going via Esbjerg I'd recommend the aquarium there. Really nicely done.
The Danes do great cyclepaths, particularly into cities. The path into Odense was especially memorable - traffic free and green all the way into the middle of the city.
Some terrific theme parks in Denmark too - not just the well known ones like Legoland and Tivoli in Copenhagen. Places like Farup Sommerland and Djurs Sommerland are both very family friendly and a pleasure to visit (and worth the schlep to get to).
Oh and the "lake district" area is lovely - all around Silkeborg is a winner.
I have some cycling maps if you're interested - PM in profile
p.s. almost forgot the tram museum near Jystrup if your little ones like trains etc. The access is by tram from a car park in the woods - brilliant fun