While I admire Queen Margrethe, however, I do feel that her decision to relinquish the titles and styles of her second son's, Prince Joachim, children was a bit 'tactless' to say the least. A more diplomatic way seems to have been to allow her second son's children to keep their titles they were born with until their deaths and any issue from those said children (her grandchildren) would be thereunto 'counts/countesses of Monpezat'.
Basically, this was a terrible decision by Queen Margrethe and it seems has caused an unneeded rift within her family that could have been all avoided.