Lenc, the only source for BMDs in Scotland is
www.scotlandspeople.gov.uk. For the period you are looking at, it is perfect as you are well within the dates that you can look up the original images online (at really reasonable costs).
Aghadowey's 1901 census looks very likely to be your family given the references to Hurlford.
Scottish birth certs from the early 1860s include the date and place of parents' marriage. Always useful if you can't find parents' marriage

Advice is to look for the birth of a child with the most unsual name you can find, in this case it will be Jemima McArdle in Hurlford 1898.
Might be a place to start...
Monica