Hi Donna,
The death details for one of the twins notes that Agnes had married again so no wonder you may have had trouble finding her.
Name: BAILLIE, DAVID SHAW
Initials: D S
Nationality: New Zealand
Rank: Private
Regiment/Service: Auckland Regiment, N.Z.E.F.
Unit Text: 15th (North Auckland) Coy.
Age: 21
Date of Death: 03/05/1915
Service No: 12/500
Additional information: Son of Agnes Clarke (formerly Baillie), of Argyle St., Avondale, Auckland, and the late John Rankin Baillie.
Casualty Type: Commonwealth War Dead
Grave/Memorial Reference: 72.
Memorial: LONE PINE MEMORIAL
But not noted on the other twin's death details:
Name: BAILLIE, JOHN RANKIN
Initials: J R
Nationality: New Zealand
Rank: Private
Regiment/Service: Auckland Regiment, N.Z.E.F.
Unit Text: 1st Bn.
Age: 22
Date of Death: 03/07/1916
Service No: 12/1545
Additional information: Son of John and Agnes Baillie, of Avondale, Auckland, New Zealand.
Casualty Type: Commonwealth War Dead
Grave/Memorial Reference: II. C. 36.
Cemetery: CITE BONJEAN MILITARY CEMETERY, ARMENTIERES
So you will be looking for Agnes Clarke instead of Agnes Baillie...unless she married after that again. Still looking for the rest although they may be in parts of Auckland that aren't online in terms of cemeteries.
Cheers
Bunny