Since a male child of hers could inherit the throne some day, it would be advantageous to arrange a marriage early, and to marry the "half-royal" back into the extended royal house, to the Hereditary Prince of Augustenborg.
Since a male heir might one day claim the throne, arranging an early marriage and integrating the "half-royal" into the extended royal family by marrying them to the Hereditary Prince of Augustenborg would be advantageous.