Even if the father had interbreeded with his own mother, it doesn't matter because that would make the both of them brothers but /also/ father-son. So the house would have an heir even if it's the result of interbreeding. I believe they are brothers.
A theory would be that the head was the result of interbreeding and since he may be infertile because of that, he adopted his youngest brother as the heir. Since they seem to have a lot of age difference, the family who needed a new head but couldn't put an infant to do the job, let the current head of the house to be the head and forced him to adopt the newborn as his as to not embarrass the family with his genetic disease or something like that.

Wait so the white haired dude is actually his "father's'" sibling? I'm not understandou