Robert, I have no problem assuming that her maiden name was Hood. My problem is that, assuming that, I could not find any father for her that made sense. There are Elizabeth Hood's but none that appear to fit her. Lydia Hood had a sister named Elizabeth but she would have been too old to be Joseph's wife as Lydia had married his uncle and her sister was older then her. There is another Elizabeth Hood but she was married to Robert Maxwell and had a bunch of children with him.
The reason I posed the question was because I cannot find anything on an Elizabeth Hood that seems to fit the profile.