My daughter also has the British Consolate Hannover Certificate and has often wondered about duel nationality; well until National Service (Conscription) is mentioned at which time the subject is usually dropped.
My son has a Northern Ireland Cert and is able to claim Eire Nationality if he so wishes as are all persons born within the shores of Ireland north and south.
... sounds like a good rotary family!
We too have one from Rinteln, one from Lagan Valley and one from Copthorne!
Turning to nationality problems, I do know of an Army mate who had some problems with his descendants - but you really have to try hard.
His son (born in Germany) married another Patch Brat - also born in Germany. Son had joined up and produced a grandchild for the Army mate - born guess where - Germany.
They did get it sorted, but after lots of paperwork, as the child and both parents were all born in Germany!