At the time, there were at least two seemingly unrelated Gothard families in the area. It actually created quite the nightmare to tease the two families apart, because they had children of similar names at similar times! I have yet to find a common ancestor of the two families. To my knowledge, they were not actually related to the photographer.
Thank you for the link to the Gothard photography business! I will have a read! I'm guessing it would be the Dewsbury location, as it was closest to their home.