Have just found these Kinvig children with mother 'Rhall'. The daughter Eleanor would be 4 or 5 in 1923.

England & Wales, Birth Index, 1916-2005
Name: Eleanor Kinvig
Mother's Maiden Surname: [smudged, but ends ‘all’. Ancestry transcribes it as ‘Bhalla’]
Date of Registration: Oct-Nov-Dec 1918
Registration district: West Derby
Inferred County: Lancashire
Volume Number: 8b
Page Number: 350

England & Wales, Birth Index, 1916-2005
Name: John Kinvig
Mother's Maiden Surname: Rhall
Date of Registration: Jul-Aug-Sep 1921
Registration district: West Derby
Inferred County: Lancashire
Volume Number: 8b
Page Number: 504

England & Wales, Birth Index, 1916-2005
Name: Mary E Kinvig
Mother's Maiden Surname: Rhall
Date of Registration: Apr-May-Jun 1932
Registration district: West Derby
Inferred County: Lancashire
Volume Number: 8b
Page Number: 577

Ancestry doesn't come up with a birth for the mother Nellie/Eleanor Rhall but perhaps it was under a different spelling as it seems to be a very unusual name.