Indeed it seems your father is my (half) brother, you are my niece (or nephew?), and I and my family begin where your story about Charles Larkin ended. 

Once, when I was quite young, I overheard mention of two earlier sons. But I never knew anything about them and in fact I wasn't even sure that this snippet of an overheard conversation actually referred to my father since my mother too had been previously married and had several sons.

I of course would be most interested in your side of the Larkin family and will try to fill you in as much as possible about my side of the family.