This name seems to be given differently in different genealogical studies. I did read, however, that the Island of Barbados had as Governors: a Chaddock, a Bell (Beall?) and a More (Moore) - which should be fascinating to Beall researchers since Ninian Beall was incarcerated in Barbados ca. 1650 - 1660.
It is quite possible that Eliz.. had been previously married before Ninian and also that her name, if Chaddock, indicates she was a daughter of the Governor. If her maiden name was Gordon, the reverse, then it is also possible that she had married the son of the Governor prior to her marriage to Ninian. I mention this because some researchers say that Ninian never married an Elizabeth Chaddock Gordon in Scotland. But perhaps she did in Barbados.
I also tend to believe that Elizabeth may have died on the island, and Ninian had the children, Mary, Sarah, Thomas who never married, and John sent to Maryland when he was able to do so (a good motive for his becoming so wealthy!).
Thomas is documented as never married, although some histories state he was Ninian's brother, not his son.The dates don't bear this out, though. Sarah probably married the Magruder. Mary and John are the questions - possibly died prior to leaving Barbados, or returned to Scotland or England, or ended up in Virginia or Maryland?
Ninian could have met or married that Mary (Polly) Moore (More) on Barbados as well. It is possible she even went to Maryland when he did, although they apparently did not marry until much later (she may have been too young at the time or they had to remarry under MD law). There has been a lot of skepticism on whether Mary (Polly) Moore ever existed. Polly was a common nickname at the time for Mary; I have seen it in other histories. There were Moores in South Carolina (Charleston) and Virginia as well.