Hello all - iluleah, Kay and Monica - thanks for the welcome and huge thanks for trying to unravel my mystery/mess!
I'll have to read and study all your suggestions - the only thing I can answer without thinking about it, is the question you asked Monica, about Isabella's death on 16 June 1945 - the informant is my husband's Granny, Elizabeth - Isabella died at her house, where my mother-in-law was born/grew up. So that's a definite! The death cert gives Hugh Cumming (gamekeeper) and Isabella m.s. Anderson as her parents. Couldn't trace them on ScotlandsPeople - I wonder if I should look further afield, England or Ireland?
My m-i-l only knew her Aunt Annie, to her knowledge there was only Annie and her mum Elizabeth. This of course wouldn't mean there wasn't another child who had died as a baby. She also knew her Granny Isabella - or Granny Broon as she was known (she was the only lady that ever visited Niddrie in a fur coat!) When I mentioned the name Jeanie Montgomery to my m-i-l it meant nothing, although it is the name her mum Elizabeth gave for her mother when she was married in 1907. Eight years later when Annie got married she gave Isabella Cumming as her mother - both marriages are definitely correct as the husbands are the right ones.
The date of birth on Annie's birth certificate, which shows her as the illegitimate daughter of Jeanie Montgomery, is also correct as it's the same as on her death certificate - 8 Feb 1897. Father is left blank, although she was given Brown as a middle name.
The dob on Elizabeth's birth certificate is one day out from the day she celebrated her birthday but not sure how relevant this is, I'm sure this kind of mistake happened, particularly if birth certificates bearing the word illegitimate were kept hidden.
The death certificates for both ladies had the mother's details reversed - Isabella Cumming on Elizabeth's (1969) and Jeanie Montgomery on Annie's (1978). Sorry if I'm repeating myself, I keep hoping it'll make sense!
Yes Monica, I agree the 1901 Census entry fits well, as does the 1891 Census from Airdrie (m-i-l knows her mother was born in the Glasgow area) - apart from the different mother. Or is she different, may be one morning Jeanie woke up and decided to call herself Isabella!
I'll have a closer look at the suggestions for James see if I can make it fit but without a marriage certificate for him and either Isabella or Jeanie, I'm not sure how I'll do that. I wouldn't be surprised if there was no marriage, I've found a few that said they were married when they weren't!
One last thing, comparing the 1900 birth certificate for Jane and her death certificate in 1903 - the informant was James Brown on both and the signatures look the same. But the mother is different - Isabella Cumming on the birth and Jane Brown m.s. Montgomery on the death.
I noticed that on Jane's birth certificate James was recorded as being in the Army Reserve - I went on to Fold3 and found papers for a James Brown, correct date, correct regiment but completely the wrong wife! Enter Mary . . . obviously the wrong James.
So many James Browns . . . so little time! But I'll keep on trying.
I am so frustrated and very thankful for all the help.