Thanks for your notes; Your details tie up closely with a family tree sketched by my father-in-law a couple of years ago. That showed William having as a son William, who had a son William = Charlotte, children William and Leonard. It sounds from your description as if that is your side of the family. I think our version of the tree has a surplus William compared with yours!
The first William had another son Stephen = Ada, children Stephen, Frederick & Nell.
I have more information and a photo believed to be the first William, which I can't post here. If you email me so I can get your correct email address, I will send it. (Click my name on this page to get my email address.) I think the address against your name on this site is incorrect as the mail is returned.