The "eingetragene Lebensgemeinschaft" was created in 2001 by law to allow homosexual couples to "marry". So the procedure is similar to a marriage in the registry office. During the last years the law has involved - before marriage was especially protected by our constitution, so certain rights simply were unavailable for same-sex couples. But when these possibilities were offered to homosexual couples, it was thought that they cannot be denied hetero-couples as well, married or not. So the law now offers certain possibilities to unmarried hetero couples as well, who can create contracts and sign them which gives them similar rights to married couples. It is not really an official status but some legal agreements which before had only been for married couples can now be made for unm arried couples as well, eg when it comes to children, their upbringing, their inheritance etc.
So, but that's merely my guess, Gustav could have gotten more rights to his children by Carina in exchange for her to get certain "widow"-rights, like a right to stay for the rest of her lif in the castle, a right to an apanage etc. Through that, in fact, Carina would have a right of staying in Berleburg and they in fact could have created a status similar to a princess for her.
But I have no more information about that, though it would make sense.
As for the will, I personally think there is ma good chance to overturn it at least in the "aryan" part. The "noble" part is up to today's interpretation hopefully, so queen Margrethe could help and protestant - we've seen with Marie and Autumn that this isn't really a problem for most people nowadays.
