This is just the result of Delphine pushing for more because she never realistically considered what the outcome of her quest would be. It was clear from day one that Queen Paola has no desire to be reminded of her husband's infidelity by welcoming his extra marital offspring into her home and at her family events.
The family of Albert and Paola is rumoured not to be on the best of terms anyway.
Yes Delphine is the victim of a situation created by her parents who were both married to someone else when she was conceived. At the same time many children grow up in much less fortunate circumstances than Delphine did. As a grown woman she should have been able to see her parents' shortcomings for what they were and move on to live her own life. She opted first for official recognition and now wants to be a Royal. Clearly not understanding what it means to be a Royal or what it would entail. What if Albert II conceived a child before he married Paola would that child dethrone Philippe and become Belgium's new monarch? Of course the government and court will have to come to the conclusion that the title of Prince(ss) of Belgium and the style of HRH are reserved to those born from a consented marriage. I wonder however if the court of justice will actually take the case on. I could very well see the judges come to the conclusion this is not part of their jurisdiction.