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Forget the 1901 marriage of Clara Lowe and Charles Smith - she married the other groom on that record:

Clara Florence Lowe
in the Derbyshire, England, Church of England Marriages and Banns, 1754-1932
Name: Clara Florence Lowe
Gender: Female
Marriage Age: 26
Birth Date: 1875
Marriage Date: 5 Aug 1901
Marriage Place: Ironville, Derbyshire, England
Father: Tristram Lowe
Spouse: Bernard Charles Watson


And the other marriage isn't right either.
Betsy Alice and George William are both still alive with children in 1911, so Ada Miller can't be their daughter. They'd had 3 children, and all are alive in 1911:

George William Smith
in the 1911 England Census
Name: George William Smith
Age in 1911: 38
Estimated Birth Year: abt 1873
Relation to Head: Head
Gender: Male
Birth Place: Elton, Derbyshire, England
Civil Parish: Crich
County/Island: Derbyshire
Country: England
Street address: Crich Matlock Bath
Marital Status: Married
Occupation: Farmer
Registration district: Belper
Registration District Number: 436
Sub-registration district: Ripley
ED, institution, or vessel: 14
Piece: 20985
Household Members:
Name Age
George William Smith 38
Batey [Betsy ] Alice Smith 40
Doris Mary Smith 9
Eleanor Gretrude Smith 4
Winifred Alice Smith 1
Hannah Maria Lowe 49

Ada Grace Millard looks to be the right Ada to be adopted by Charles Smith particularly with Joseph and Mary Ann as parents.

I still can't see a death for Mary Ann Miller though.

Choccy suggested a 1902 Derby death for Mary Ann using surname Smith.

Copying here again:


Deaths Sep 1902
Smith Mary Ann 33 Derby 7b 302