Thank you for sharing the announcement from the Danish Royal House! That answers my question about whether Gustav and Carina's use of "Hereditary Prince of Sayn-Wittgenstein" for their son on the invitation was a one-off, since their son is only called "Prince of Sayn-Wittgenstein-Berleburg" here.
The announcement actually refers to Prince Franz-Albrecht and Prince Carl-Anton as Highness, rather than Royal Highness. Can anyone identify which family Carl-Anton belongs to? (ETA: Thank you to Adda for identifying Franz-Albrecht.) Note that the German predicates of Hoheit and Durchlaucht are both translated into Danish as Højhed (Highness), whereas English speakers would ordinarily translate Durchlaucht as Serene Highness.
Could the Danish speakers explain the difference between "faddere" and "gudforældre", which are both translated into English as "godparents"?
faddere is meant like the sense of supporters, gudforældre is godparents