Theoretically we could have a divorced unmarried President enter the White House and designate his teenage daughter as 'First Lady' in that she does the same job as the wives of Presidents, in charge of formal hosting, doing charity work, taking up a cause, etc, and she would count as a 'legit' First Lady by the definition of the ceremonial, unofficial role.
As stated above, two teenage First Daughters DID serve as unofficial First Ladies when her mother was alive but ill. Helen Taft Jr. starting age 17 (and she
dropped out of school to do so!) and Mary Fillmore starting age 18. In contrast, the 10 year old Ellen Arthur was passed over, and her married aunt called to Washington to fill in for both First Lady and Ellen´s mother.
There actually was a wife of President who never was to Washington. Anna Harrison. Aged 65. Due to illness, did not show up at inauguration. Planned to travel to Washington in May. Instead, a 37 year old widowed daughter-in-law served as First Lady... and William Harrison died before Anna got packed to set out on voyage.
Two more wives of President who largely did not work as First Ladies:
Jane Pierce. Chronic depression. Stayed in her living rooms in White House for first two years of her terms. Delegated the functions of First Lady to an unrelated good friend... who happened to be wife of Secretary of War.
Yes. Varina was the First Lady of both Union (unofficially) and Confederacy (officially).
And Eliza Johnson was chronically ill with tuberculosis in White House. So her married daughter Martha Patterson, 37 at inauguration, served as First Lady.
To return to the issue of age qualifications:
17 is old enough, because Helen Taft Jr. served at that age, and was only not quite official because Sr. survived.
10 is possibly too young, because Ellen Arthur was passed over. Though her personal dislike of publicity may have contributed. Certainly Ellen Grant, ages 13 to 16, held a high public profile (with her mother around) that Ellen Arthur did not get by age of 14.
Would the Ellen Grant whom father declined to rebuke when public critizised her for dancing all night before age of 16 have been appointed First Lady if Julia was unavailable?
20th and 21st century USA quite officially has Office of First Lady.
How would Office of First Lady have been supposed to operate if, on 20th of January, 1993, they were facing inauguration of a 12 year old First Lady - Chelsea would only become a teenager on 27th of January, and as per PoD, Hillary would have died late in campaign or before inauguration... leaving the 12 year old Chelsea as the woman of the house, and of White House at that?