Hamburg and Luxembourg

Luxembourg is a bit of an outlier, but Hamburg is right on the way.

Where were you thinking of starting and ending? And how much time will you have?

First of all Luxemburg does not make geographical sense if you are travelling between Amsterdam and Copenhagen, but Hamburg does. However unless you are dead set on taking the train, flying between Amsterdam and Copenhagen is both faster and possibly cheaper, Norwegian Airlines usually have good deals on this route. You don't say how much time you have, so it's hard to answer if you should spend more time in the other countries, but the short answers is, that these countries are more than their capitals and it should'nt be hard to find something worth seeing.
If you have to train it, I would probably recommend Lübeck over Hamburg, but it depends on your interests.

The kids would probably get a kick out of Hamburg's Miniatur Wunderland.

Thank you for all responses. We will be there for 14 days. I like the idea of flying from Amsterdam to Copenhagen as it is very inexpensive and quick.
So, if we do
Bruges
Amsterdam and Copenhagen, is going to Berlin too much, any other ideas? We would like to give our kids a first taste of places and only have time to travel once a year.
Thank you

Your original post mentions Brussels and now you mention Bruges. Is this a typo or du you intend to see both? If you want to see both, they are close to each other, so either could be done as a day trip.

The 14 days, is that including travel time from home or days on the ground? If it's including travel time, then you only really have 12 days and you should also consider the time spent packing, unpacking, getting from the hotel to the airport/train station etc. This could easily take half a day of you precious time. If it was me I would stick to 3 cities (Brussels, Amsterdam and Copenhagen) and consider day trips from there if you want to see more. That could be Bruges from Brussels and from Copenhagen one or more of the usual suspects Roskilde, Hillerød and Helsingør. I'll leave Amsterdam to others.
I would not try to ad Berlin to an already tight schedule, since you will waste time moving cities and since Berlin has more than enough to keep you occupied for at least a week.