Looks like a mistake has been made when registering Emma's birth by including Margaret's previous married surname of Leigh rather than her maiden name of Vernon
I think you have all the pieces in the right order.
Margaret born in Hulme to parents John and Martha c. 1840
Married John Leigh in 1859. He died in 1869. At least two children from the marriage (likely more?). 1861 census shows Sarah Ann, 4 months old and John Henry, aged 2. Do you know what happened to them?
Have you found Margaret in 1871? No sign of a marriage but Margaret starts having children with Joseph Platt and shows as his wife from then on.
I think the John William Vernon lodging with Margaret in 1891 is likely her nephew, son of Joseph.
You will have all of these entries I am sure, but just adding here for additional info:
Margaret in 1851 with her family including brother Joseph. The first four entries show Cheshire birth places and the rest Hulme Manchester:
John Vernon 36
Martha Vernon 39
William Vernon 18
John Vernon 15
Margaret Vernon 11
Joseph Vernon 7
Mary Vernon 4
Betsy Vernon 1
Brother Joseph with son John, born in Blackley, in 1881 9 Southern St, Hulme :
Joseph Vernon 39
Ann Vernon 28
John Vernon 10
Charles Vernon 8
Esther Vernon 6
Martha Vernon 4
Mary Vernon 2
However, and there seems to be lot of these here
, Joseph is showing as a house painter by trade, not a steeple jack.
Monica