Hope you can unravel something from these Census entries:
CENSUS 1901:Ayrshire,New Cumnock.
At Bank Terrace Village:
-Alexander SEATON,head,mar,35,Coal Miner,b.Ayrshire,New Cumnock.
-George Gow COLLIE,boarder,unm,21,Electrical Engineer,b.England.
And next door:
-Thomas HADDOW,head,mar,57,Coal Miner(Retired),b.Dumfries,Sanquhar.
Checked the Census before:
CENSUS 1891:Ayrshire,New Cumnock.
At 8 Connelpark,Connelpark:
-Thomas SEATON,head,mar,52,Coal Weigher,b.Kirkcudbright,Dalry.
-Alexander,son,unm,25,Coal Miner,b.New Cumnock.
-James ,son,15,Coal Miner,b.New Cumnock.
-Mungo WALKER,son,16,Coal Miner,b.New Cumnock.
-David WALKER,son,12,Pony Driver(Underground),b.New Cumnock.
At Bank Glen Cottages:
-Thomas HADDOW,head,mar,47,Coal Miner,b.Dumfries,Sanquhar.
I checked the 1891 Index for the rest of Ayrshire,and surrounding Counties,but no sign of Annie or Gladys .
Is it possible that the Jessie,9,in 1901 was your Grandmother?Jessie,generally,was used as an alternative to Janet,and occasionally Jean.