I had a little eureka moment. Using the date of the last census when William was shown living with son John in 1891 and the fact that he wasn’t on the 1901 census, I searched for his death record between those 10 years and found a William BARTON who died in Carlisle in 1896.
Then I started to think about what I had written about Mary MCINTOSH possibly being a relative of Jane’s. So I did a search for a marriage record for William and Jane with a 10 year spread from when son John was born. When you use Ancestry.com you can see the names of other people who are in the register at the same time as the person you’re looking for. So I kept looking for William and found a record from Bolton, Lancashire. Remember reader, that John BARTON was born in Bolton.
Then came the eureka moment. There they both were on the same page - William BARTON and Jane MCINTOSH married in 1837 in Bolton. I was right, Mary could have been her mother or grandmother and the other Mary maybe Jane’s neice.