I think your mother’s information is true!
I’ve found Charlotte Haigh’s birth in Huddersfield – she was born at Paddock, Huddersfield on 13 December 1904 and baptised at Paddock All Saints Church on 26 February 1905. Her parents were William and Mary – William was a greengrocer.
In the 1911 census, Willie Haigh was a ‘carrier of goods’ and the family lived at Market Street, Paddock. Willie and Mary were both aged 25 and Mary was born in Scotland
They were married in Huddersfield at the beginning of 1904 – Mary’s maiden name is shown as Thompson. I think Lottie may have died in 1929 but I haven’t found her burial.
Le me know if you’d like any more information