Hmm. What if Battler's sin is actually a lot worse than a broken promise?
I'm sorry, but what I'm alarmed by is that Battler's sin is 6 years old, and Ange is six years old.
From a genetic standpoint, let's think of it this way:
(Assuming no hair dyes have been used
*Kyrie does not have red hair
*Rudolf does not have red hair
*Asumu's hair color is...?
*Battler's hair is red.
*Ange's hair is red.
Red hair could be a recessive gene. Therefore, if both Kyrie and Rudolf have recessive red-hair genes, then it's possible for the kids to have red hair.
Ange is the daughter of Kyrie and Rudolf. At least, that's what we're led to believe.
It is very unlikely that Kyrie and Rudolf gave birth to two red-haired kids.
The odds are much more likely if Battler were to... you know.
What if... oh god... this is going to sound absolutely terrible.
I suspect that Battler had sexual relations with another female character on the show. This could very well have been Shannon, and Ange is Battler's sin. After all, if Shannon gave birth to Ange, then Shannon would have been 10 years old. I believe that this is old enough for childbirth, albeit barely.
This conforms to the Shannon-Battler relationship, as well as explaining the circumstances behind Ange's birth (the six years coincidence).
One problem with this is this red truth:
Ange is Battler's brother.
Even though they weren't in the same generation, they could have treated each other like siblings.
...I'm not trying to be a pervert here, just bringing to light an observation.
If Jessica and Battler did love each other, yet Battler got close to Shannon to make Jessica jealous, this could come about.
After all, he is Rudolf's son (a pervert).
Eh, what do I know. My original idea was
Battler impregnated his own mother.
...Or, it could very well have been
Battler left the family registry because Rudolf impregnated Kyrie.
Maybe the six years coincidence is just a red herring.