When the current duke dies,it will be up to his son and his brother as to claiming the title.
The son's claim will be refused based on the existing public record unless he can call compelling evidence to the contrary. That is unlikely as he should have had such evidence when the trust case was decided in 2011.
In all probability there will be no application by him, but there will be one by the present's dukes brother.
He will have to prove that at the date of his death the his death present duke had no legitimate male heirs, so as to enable him to be enrolled on the Roll of the Peerage.
Until there is legislation to the contrary, English law,as one of my law lecturers pithily described it is contained in the maxim "once a bastard,always a bastard".