In 1869, for Grant's inauguration, Grant refused to ride with President Johnson...

[steve2470]

On March 3, the President hosted a large public reception at the White House on his final full day in office. Grant had made it known that he was unwilling to ride in the same carriage as Johnson, as was customary, and Johnson refused to go to the inauguration at all. Despite an effort by Seward to prompt a change of mind, he spent the morning of March 4 finishing last-minute business, and then shortly after noon rode from the White House to the home of a friend.

https://en.wikipedia.org/wiki/Andrew_Johnson#Completion_of_term

From what I've read of Johnson and Grant, I cannot really blame Grant. Johnson pulled a Trump, which was inexcusable to me.

Do the President and President-elect ride to the ceremony in the same vehicle these days ? Does anyone know ?