It is a very hard an complex issue to discuss but I will try anyway!
I tend to think that the Danish government and people were wrong in assuming that the Duchies belonged to them.They had a common sovereign, the king of Denmark also being Duke of Schleswig-Holstein. This happend because King Christian I way back in the 15th century was elected King of Denmark an separetelly elected Duke of Shleswig-Holstein after his uncle. He promised that the Duchies forever would be united for all times, and that Schleswig never became a part of Denmark...so far so good!
When it became clear in the 1830-, that there was a great posibility that the older danish line of Oldenburg would die out in the male line, thats when the problem started.
The danish throne would then pass to a female line of the family, (later) Queen Louises mother, Princess Charlotte.
The duchies of SH didnt have female succession, so the next in line there, according to many people, where the eldest line of the younger oldenburg line, The House of Schleswig-Holstein- Sonderburg-Augustenburg. The Danish kings didn't want this to happend, so they violated the original saying, and tried to bring the more Danish minded Schleswig closer to Denmark, and ignoring the Augustenburgs claims.
This caused many other problems(to long to discuss all the events in detail

), such as the first war of 1848-1850. The augustenburg family where exiled, and eventually Christian was elected as future king. when he became king he was forced by the public to sign the new constitution of Dk, wich ment that S would become a part of Denmark.
I think this was wrong, and the overall people of SH didnt want this to happend. The wanted to be independent and together...
I think that the Danish people of that time, including the royal family where ruled more by their emotions then what was right.
As far as Germanies concern, they to violated the rights of SH, but they could only intervene because the Danish goverment broke the international deals.
SH, should have become an independent state( as they also where under the danish dukes!), and the head of the country should be chosen by the people.
Just my humble say in this!