www.scotlandspeople.gov.uk is your first port of call.
There is a birth of Alice McManus Alcroft in Monkton and Prestwick in 1921. Would that be your mother? She died in Prestwick in 1982 aged 66, mother's surname Alcroft.
I note with interest that an Alexander Alcroft married an Annie McManus in Ayr in 1900, and that in 1901 there is a family in Ayr consisting of Alexander Alcroft, 19, Riveter, born Paisley, with wife Annie, 20 born Ayr and son John, under 1 year, born Ayr.
There are five deaths of Alcrofts, mother's maiden surname McManus:
John McManus, 81, 1981 - born 1900
Rebecca Jones D, 26, 1929 - born 1901
Alexander, 74, 1981 - born 1907
Annie McManus, 95, 2010 - born 1914
James McKenna, 81, 1999 - born 1917
John McManus married Margaret Semple or Hamilton in 1924
Rebecca J Drisc... married William Lucas in 1926.
In the 1911 census index, the following are listed on the same page of the book in Port Glasgow:M Margaret, 54; Annie, 31; Alexander, 29; John, 11; Rebecca, 9; William, 6; Alexander, 4; Frederick, 1. You can view the original to get all the information on it.
In 1891 Alexander Alcroft, 11, is in Newton-on-Ayr with his mother Margaret Anne, born England, older brother John Henry, 14, born England, and four younger siblings.
Margaret Ann Driscoll or Alcroft, 79, died in Monkton and Prestwick in 1936.
William Henry Alcroft, mother's maiden surname Nicoll, died in Ayr in 1894 aged 38.
William Alcroft married Margaret Ann Driscoll in Birkenhead, Cheshire, in 1877.
In the 1971 census, Margaret A Driscoll, 14, is in Birkenhead with her father Alexander Driscoll, 40, born Ireland; mother Rebecca, 40, born Lancashire; and four siblings.
Margaret Ann Driscoll, mother's maiden surname Jones, was born in the Wirral in 1856. Alexander Driscol married Rebecca Jones in Liverpool in 1849. So it's easy to see where Rebecca's middle names came from

Not quite sure where William Alcroft came from.