Thank you, I did know this back story, and have actually read the biography that caused all the publicity, but I still think that dragging this out, rather than acknowledging that Delphine was his daughter (which, even from your account, the King knew very well to be the case)has made the "optics" of the situation far worse than they needed to be.
He had been in contact with Delphine most of her life. If the stories are correct he and Paola even considered a divorce. It was his brother King Boudewijn who made it clear that if the princes de Liege were to divorce they would both loose their children, their dotation and they would no longer be part of the Royal Family.
The very devout Boudewijn and Fabiola could not accept a divorce and made the terms unacceptable for Albert and Paola.
The couple decided to try again and surprisingly enough did find their way back together again. Faith seems to have played a role in it but it cannot be all.
Albert stayed in contact with Delphine even after he was unexpectedly called to the throne. Only after a biography about Queen Paola publicly stated something most royalty-journalists already knew, that Albert had fathered a child outside his marriage, did things derail. Delphine and her mother were quickly discovered and she started to use her status as the royal bastard [im using this term simply in the meaning of child born out of wedlock and don't intend anything other with it]. As an aspiring artist her link to the king helped her get expositions. At the same time she and her mother must have felt left in the cold when Albert returned to his legal family and they wanted recognition.
I suppose Albert could have done what the other Albert II (of Monaco) has done and publicly admit he is the father but unlike the sovereign prince of Monaco the King of the Belgians was not a bachelor but married to the woman who he had betrayed and who was now Queen. She and their daughter Astrid (the only one of the three children said to be close to her parents) may have weighed in on the matter as well.
Why Delphine has pressed on for this DNA evidence i don't know. Her resemblance with Albert's mother Queen Astrid, his sister Josephine-Charlotte and niece Marie-Astrid is uncanny. She looks more like them than any of his children with Paola.
I don't believe she has any doubt on who conceived her. So pressing for DNA evidence must have another motive.
I do wonder why King Albert did not resolve this situation sooner. Does anyone have an explanation?