Although the United States does not have a nobility class there are still people who were considered the natural leaders of the nation. This often would include the children of what was considered the elite and these elite would include the descendants of major political leaders. As Americans we like to believe that anyone can raise to the top ranks of power, however, this is only some what true.
His grandson Thomas Jefferson Randolph was a Colonel in the CSA and another grandson George Wythe Randolph was briefly Jeff Davis' Sec of War. Several others also served the CSA.
On the other side were some of Sally Hemmings grand kids. Beverly and John Jefferson served in Union (white) units with John making the rank of colonel./ Several others served in black units including the 55th Mass.
One of John Tyler's sons , Robert, was not military but was Register of the Treasury for the Confederacy. His younger brother John Alexander was too young to join the army but his mother let him join the CS Navy , I think.
Like Washington, Jackson had no children but he adopted one of his wife's brothers sons. He was re-named Andrew Jackson, Jr. He was too old to fight when war came but remained loyal to the union. His wife's sympathies, however, were with the south and their two sons fought for the Confederacy.
Jackson also raised another of his nephews, Andrew Jackson Donelson. He was not formally adopted, however. Donnelson's children also had divided loyalties. One served as a staff officer for Forrest.
Archibald Harrison was the Lt. Colonel of 27th Indiana Infantry Regiment. His grandfather was President William Henry Harrison. He was a brother to future president and brevet brigadier general Benjamin Harrison.
Correct. Robert wanted to serve, mother Mary didn't want him to, eventually he was made a captain and assigned to Grant's staff. This was late in the war, relatively safe, and not far from Washington. As I understand it, neither President Lincoln nor Robert thought special provision should be made for the President's son while so many others - and their mothers - had no such option.