Even if seat reservations are not mandatory between Copenhagen-Hamburg-Prague on the 22nd of December I highly recommend you to make reservations. Otherwise you don't have a guaranteed seat and you might have to stand. If the train is too crowded you even might have to leave the train.

Deutsche Bahn expects high demand that day and you only have one connection that will get you from Copenhagen to Prague during the day. Leaving Copenhagen at 8.56 and arriving in Prague at 21.35. Changes in Fredericia, Hamburg and Berlin. 

You make your seat reservations at bahn.com. and use the option "seat only" to only get a seat reservation. The cost is 4.50 EUR per person. 

In all trains with optional RES all seats are generally marked for the sectors they are RES for. That is: if the system works properly, on which there is never no 100% garantee. Chance on finding several seats for a family together are nil. Plus that this may change after every stop.

for the very few and too short direct trains Cph-HH: use dsb.dk, most often bahn will not work for that. Agree with anna: on THAT day it will be very busy. The week between Xmas and 1/1 tends to be very quiet in most cases-except for those returning from Xmas and those going for their 1/1 celebrations just after/before.

bahn.com works fine, as long as reservation is optional, which is outside the summer.

Copenhagen - Prague can be booked for €4.50 per person for the whole journey.

There's also an earlier possibility, with only one change:

Deutsche Bahn expects high demand that day and you only have one connection that will get you from Copenhagen to Prague during the day. Leaving Copenhagen at 8.56 and arriving in Prague at 21.35. Changes in Fredericia, Hamburg and Berlin.

There's also an earlier possibility, with only one change:

 

Thanks @rvdborgt I had set the departure time to 8.00 so that's why I missed it. 

All seat reservations for the 7.26 departure from Copenhagen to Hamburg on the 22th of December are already sold out. 

The seat reservations on the 8.56 departure are also sold out between Copenhagen and Fredericia, but you can travel on the train without a reservation and stand. From Fredericia to Prague there are at the moment seats available at bahn.com but I recommend you to make reservations as soon as possible. 

The quickest way to check availability of seats between Copenhagen and Hamburg is 

https://travel.b-europe.com/dsb-rail/en/reservation-only#TravelWish

Please note that you need to proceed to the booking page to get information whether seats are available or not. On the first page all trains are shown with prices even if no seats are available. 

@Harpreet Singh There is a Swedish train vacation Facebook group (Tågsemester) where one member updates a pdf with detailed description of the different possibilities to travel between Copenhagen and Hamburg.

https://m.facebook.com/groups/tagsemester/permalink/3499618833591040/?m_entstream_source=group&paipv=0&eav=AfYSJd1eVv8pZHLtE63a9g9RWy0kYqRuFmptFhMhqKbHvezgRe4WRAcVo9hmuIrtmFQ

Thanks AnnaB. I have made the reservations now for a peaceful journey : ). Will do the same for the return journey as well.