Hi Kylie
I'm now at home and have my stuff in front of me. Richard Dawbarn (1786-1827) was the fourth of 11 children of Richard Bunbury Dawbarn (1757-1829) and Elizabeth Saltenstall. RBD was a preacher in the Hill Street Baptist church and may have been one of its founders.
All of the info you posted about Mary and Richard matches what I've got except I have an extra child, Martha, who was born between Emily and John Stephenson on 7 May 1823 and died 14 Jan 1895. I'm descended from Richard Wood Dawbarn, the fourth child (this family was spectacularly unoriginal with children's names), and Mary Lafone Dawbarn (his cousin).
I've traced the Dawbarns definitely back to the start of the 17th century and slightly less securely back to the 1540s. It's a rare name and virtually all of them that I've found have turned out to be related to me.
I have copies of the wills of Richard Bunbury Dawbarn, Richard husband of Mary Wood and John Dowson, if these are of interest. My great-uncle (whose middle name is Dawbarn) has some paintings of early Dawbarns: Richard Bunbury D., Richard Wood D. (b. 1814), Mary Lafone D. his wife, and John D., brother of Richard the husband of Mary Wood. Unfortunately he doesn't have any of Richard and Mary, but I have photographs of the others if you're interested.