Sasha,
I'm sure this will be a big help in my sorting out these two families. If Susannah Hayden Overill is my 3rg Great Grandmother she was only about 17 years old when she married Joseph Bradford, but she seems to be the only candidate.
The two Bradford children you found are, I think, the children of Joseph's brother, James. Like Joseph, his family seems to disappear for the 1841 and 1851 census.
So my hunt continues (nothing new for us genealogists), but thank you so much for your help, it's greatly appreciated.
Kind regards,
Shaz