Yes, that makes the family structure

Much clearer and it also makes Doctor Berry much more interesting historically than he first sounded.

If your grandmother's uncle was Doctor Berry, then to your father he was a great uncle and to you a great great uncle.

More unused unusually, Barry's daughter then married Mehdi, your grandmother's brother.

So Mehdi appears to have married his own first cousin.

Their sons are therefore your father's first cousins, and Barry's grandmother,