Random minor realisation.
Rudolf was "in elementary school" when the family already lived in the mansion. Mansion was completed in 1952. School in Japan starts at 6 years of age, elementary school continues for six years afterwards. It is therefore not possible for Rudolf to have been born earlier than 1940. He cannot have been younger than 20 at the time of Battler's birth, as he needs to be an adult for that, so latest possible birth year is 1948.
Japan was in the war between 1939 and 1945. While in Ep7 Kinzo says he wasn't drafted due to influence of the family elders, he nevertheless volunteered. It is not said exactly when this happened, but generally, birth rate drops during a war not only because many men are drafted, but also because families don't like to raise children in an economically and politically unstable situation, so being born during the war is in itself somewhat doubtful.
But the kicker is... That leaves Rudolf only two time windows to be born from Kinzo -- after 1940 but before Kinzo volunteered (so Kinzo went off with the intention to be killed when he just got a third child, the bastard) or after Kinzo was demobilised (no earlier than 1945) but before 1948. Now
that time window is definitely while Beatrice Castiglioni was still alive.
That's even worse than with Rosa, what gives?
Is Rudolf even Kinzo's son?