When visiting Copenhagen, you couldn't be in a better location than at Melanie's house, especially with children. The house is in a very quiet location, and yet at 10 mins to the city center by public transport (train is 5' by car and 15' min by foot from the house). We alterated going to the city and staying at home to go walk in the park nearby or play on the beach... The children loved they could just play on the street freely, or in the adjacent woods.
In the house, you will find everything you need. The kitchen is well equiped, there was a big duplo box to play with, ... We could make use of the bikes to go to the bakery or store, which is a lot easier in the area than taking the car :) When your children are bigger, you can even take the bike to the city - which would be a perfect way to visit the city as well.
The only point of attention would be that the rooms are quite light, so our children had some difficulties sleeping in the beginning, as they are used to sleeping in complete darkness. But once we bought eye patches that "issue" was resolved... :)
We had a lovely vacation, thanks to the great located house! Totally recommended!