Probalby if he had not rejectied Delphine she would never have progressed to what she did, and ended up as a Princess. So his arrogant heartless behaviour has had the exact opposite effect to what he hoped for. He is less liked than ever and she is now recognised as his daughter and has a royal rank....
Her lawyers saw the loophole in the badly worded royal decrees of 1991 and 2015 and figured they would win in court if they petitioned to have Delphine recognized as a princess. Under those circumstances, I think Delphine would have gone for the title regardless of the status of her personal relationship with Albert and the rest of the family. Obviously being an HRH is something that matters to her.
As for the RF's reaction, I think they are being pragmatic, probably under the advice of the courtiers. They have been beaten in the courts with no prospect of a successful appeal and public opinion seems to have sided with Delphine, so the best solution in damage control is to be seen as extending an olive branch to the enemy. The Crown must always win above one's own personal feelings.