I have the 1841 Middle Calton census with an Adam Williamson and Barbara Burton, both born ireland, with 4 children, James 15, John 15, George 10, cant make out the last name age 8
George is exactly the right age to be the one who was listed with Jane Peel in 1861. However his age is transcribed as 20 by both FreeCEN and SP. Can you post an extract from the cenus showing the family's names and ages?
I also have MC 1859 for John Burton Williamson and Margaret Peel
Parents Adam Williamson dec, Barbara Burton alive then but died in 1883 Bridgeton
both of margaret's parents are dec. Isaac Peel and Mary Muir could be Isaac second wife
In the censuses Jane and Margaret are a few years older than Anne and Elizabeth. It looks to me as if Mary Muir might be Isaac's first wife and Christina/Constance his second wife.
Or possibly Jane got her mother's name wrong when she got married. Was she able to sign her name? If she couldn't read and write, she wouldn't notice an error.