That is the whole problem: that button doesn't show up! I moved over a dozen different combat units on and off the square with the princess several times. The button outlined in red in the above screen shot never shows up, no matter what I do.
I captured the city once and couldn't move her, then reloaded and razed the city, with no change. The only time the princess did move was after a city razing and subsequent peace treaty when the princess' original civ told me to get out. She moved automatically with my troops, but then just as before, could not be moved from her spot.
Looking further through the forums, I saw a thread called "Capture the Princess don't work" that has the exact same problem I experienced, and none of the solutions suggested there worked for me either.
I would post a screenshot, but I gave up on that game already and don't have any saves from it. Suffice to say, I tried everything I could to fix the problem before coming here, including reinstalling the whole game.
Thanks for the help, though