can someone explain the cousin thing on ch 37 pls? Im a bit dumb rn

From my understanding, the previous duke and duchess (now ex-wife) are cousin. The ex-wife had an affair with a commoner knight, thus the current red-haired duke was born.

So basically the current duke does have the blood of the duke family even though he's not the duke's biological child, since his mother and previous duke are still in the same family tree, cmiiw

Do u get it? Sorry if this is kinda confusing ╥﹏╥