For that short time I would do one of two things. The first is staying in Denmark, maybe crossing into Sweden, but pretty much use Copenhagen as a base. You aren't spending any time dragging luggage from hotel to hotel if you stick to one base. You can still cover a broad geographic area. But you posted Germany, so I am guessing that is your preference. Still, as Hamburg's biggest fan, I recommend you stay in Copenhagen. You can explore the city, go up to Helsingor (and take the ferry to Helsingborg in Sweden) for the Hamlet castle, or cross the bridge to Malmö. That gets you two countries (if that is important). You can visit Roskilde or other regional sites. Furthermore, my guess is your flight out is early enough on April eighth that you will spend the night before in Copenhagen. So you really only have four full days on the ground, and there is enough to see and do in and around Copenhagen that you can easily spend the time just in Denmark. You could venture over to Odense, Aarhus, Billund (home of Lego if that is of interest), or some of the Viking sites if you are particularly ambitious.
My thought if you are doing Germany is to take a train to Hamburg on April 3rd. That's all you are doing. It is a 4,5-5 hour drive from CPH to HH and about the same by public transport, and driving while jetlagged is NO fun and certainly less than safe.
If you want Germany, I would use Hamburg as a base. You have huge architectural variety in HH, but you can easily do great day trips to places such as Bremen, Lübeck, Schwerin, or Lüneburg. Your trip is so short, going any further than Hamburg is absolutely going to make you spend the whole time driving. You don't need a car for that, either. Each of those is a very pleasant day trip by public transport--and they are architecturally diverse.
You would have the 4, 5, 6 in Hamburg. That isn't much time. Then you are back on the road to Copenhagen, losing the better part of a day on the road again. Of your five days, you have now spent two mostly driving through pretty but not particularly scenic or interesting countryside--the same stretch twice.
But if you really want to come to Hamburg, I can devise a pretty good personalised itinerary based on the interests of you and your kids.
And precisely NONE of those places has anything related to high rises or new cities.