I do realise this is an old thread bur I'm new here so bear with me as I confuse matters more.
When Danish royal titles are translated into English it will be Prince/esse of
Denmark. This is not incorrect but in Danish we use 2 different prepositions depending on the person's place in the line of succession.
Frederik is Crown Prince to
Denmark ('to' because the throne will most likely be his one day)
Mary is Crown Princess of Denmark ('of' in her case because she came by the title by marriage)
The Duke of Edinborough is also Prince of Denmark (he is the decendant of a Danish king but no longer in the line of succesion).
Interestingly Joachim's and Marie's children are no longer 'to' but 'of' Denmark.
People are speculating that Nikolaj and Felix will inherit their mother's title and be counts of Rosenborg. Or their future spouses will be Countesses of Rosenborg. This is purely specuation!
Nikolaj, Felix, Henrik and Athena are still in the line of succession but it will take a tragedy of epic proportions for either of them to take the throne and maybe that's why they are 'of' rather than 'to' Denmark.