Here's where I am at the moment, having had a night to sleep on it. Thanks for all your suggestions which have got me thinking more carefully about this. I think I am guilty of making the mistake of taking census information as verbatim.
James Renwick's first wife Ann was born 1795 in East Boldon, Northumberland. She died 1842 in Long Framlington and was buried in North Sunderland. James then married Mary (I still have not found their marriage) and what is not in dispute, on the evidence of future census returns, is that she was from Scotland, possibly Musselburgh. They had 5 children born from 1844 to 1850, variously around Bamburgh, Lucker and Shilbottle, Northumberland.
Then the 1851 census is taken. James may have become confused when the enumerator asked for his wife's place of birth and gave that of his first wife. Then, having added Musselburgh, the enumerator wrote down what he heard - Muchelborough.
Does all this make sense? I would welcome your comments.
What is left is for me to find out where and when James Renwick married Mary. She was born around 1802 but I have been unable to identify her birth anywhere. If she was a widow when she married James I reckon I'm probably up against the proverbial brick wall.
Regards, Jack