The math makes no sense. If the duke is 24 and he hadn’t seen his girlfriend in more than 12 years and Riri is 10 that would mean it not possible for Riri to be his daughter biologically and also he was having an affair at age 12.
This is such a bad cover story that I suspect it’s a mistranslation. There’s no way nobody would realize that a woman he hadn’t seen in 12 years couldn’t possibly give birth to his 10 year old daughter.