Michelle,
Benedikte's children do not carry out duties for Denmark. The children do not have succession rights (although there are views that they might) due to qualifications set up at the time of the marriage. Benedikte's children would have need to be educated and raised in Denmark (there were more qualifications as well) in order to have succession rights. Gustav was born in Germany. He is a citizen of Germany, not Denmark. The two girls were born in Denmark, but did not have Danish citizenship because their father was a German citizen. Both aquired Danish nationalty as adults. Gustav's future will be involved with Berleburg (actually, he already owns the estate - for tax purposes the estate was turned over to him a few years ago.)
Frederik IX did give the HH to Richard and to the three children - it is their rank in Denmark, rather than serene highness, which doesn't exist in Denmark.
