It seems this was a major fear during his youth that Crown Prince/King Frederik (II) of Denmark would marry his mistress, Anna Coritzdatter Hardenberg. Even once he became king, he pursued the course unsuccessfully, but eventually caved to pressure to marry a princess, namely Sophie of Mecklenburg-Güstrow.
What were the major reasons behind it? Wikipedia just says that Anna was already betrothed and that many of the king's ministers advised against a domestic marriage. But it also seems (from her wikipedia article) that Anna was ambivalent about the match, since she seems to have been rather relieved when the king left her alone, and she was one of the voices who encouraged him to marry abroad instead.
So, say Freddie decides to emulate Henry VIII and his cousin, Erik XIV over the Sound, and marries Anna Hardenberg. When is the most likely time this marriage would occur? Would there be children (Anna didn't have any OTL, but she might have been close to menopause by the time she wed OTL)? Would Frederik stay "king"? Or would the Danish nobility do the same to him that the Swedes did to Erik?