AHC: Make other presidential "princes"

There's been two presidents who've been the son of another president-John Quincy Adams and George W Bush. We know of their families. We also know of other presidential families who threw their hat in the ring when it came to the presidency, such as Robert Taft. But what about those that didn't? Your challenge is to make a situation which might lead a child of a president to try and become president themselves, maybe even succeeding. The POD is at earliest the day after they leave office, and they have to be politicians IOTL.

Possible choices are John Van Buren, David Gardinier Tyler, Frederick and Jesse Root Grant, James Rudolph Garfield and Herbert Hoover Jr. For it to be an actual challenge you can't choose the Roosevelts, Kennedys and Tafts, they've been overplayed and are big enough for their own threads. Robert Todd Lincoln can be considered, but you don't have him become president because he was VP when the current president died
 
John Scott Harrison

Son of President William Henry Harrison

Elected to the US House of Representatives from Ohio in 1852 as a Whig reelected in 1854 as a member of the Opposition.

(POD) He wins his 1856 reelection campaign as a Republican and again in 1858.

He then manages what Benjamin Wade or Salmon Chase could not do. Namely, unite the Ohio delegation behind him going into the 1860 convention. Seward falters as in our OTL and Harrison's now four terms of service in Congress and moderate image gives him the needed edge over Lincoln.

Young Tippecanoe wins the 1860 election thus becoming a second generation US President.

The Harrisons become the only family in US history to have three Presidents when John's son Benjamin is elected to the office in 1888.
 
John Scott Harrison

Son of President William Henry Harrison

Elected to the US House of Representatives from Ohio in 1852 as a Whig reelected in 1854 as a member of the Opposition.

(POD) He wins his 1856 reelection campaign as a Republican and again in 1858.

He then manages what Benjamin Wade or Salmon Chase could not do. Namely, unite the Ohio delegation behind him going into the 1860 convention. Seward falters as in our OTL and Harrison's now four terms of service in Congress and moderate image gives him the needed edge over Lincoln.

Young Tippecanoe wins the 1860 election thus becoming a second generation US President.

The Harrisons become the only family in US history to have three Presidents when John's son Benjamin is elected to the office in 1888.

I agree that this is the most probable option given the extremely narrow terms of the AH challenge. Sons of Presidents generally don't make much of themselves. They either become corrupt, die young, or crash and burn when they take their own swing at electoral politics.
 
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