The Sabine Women might qualify
Consequently, the Romans planned to abduct Sabine women during a festival of Neptune Equester. They planned and announced a marvelous festival to attract people from all nearby towns. According to Livy, many people from Rome's neighboring towns attended, including folk from the Caeninenses, Crustumini, and Antemnates, and many of the Sabines. At the festival, Romulus gave a signal, at which the Romans grabbed the Sabine women and fought off the Sabine men. The indignant abductees were soon implored by Romulus to accept Roman husbands.2
I'm not sure why OP rejects Mary Queen of Scots
James Hepburn, 4th Earl of Bothwell, was generally believed to have orchestrated Darnley's death, but he was acquitted of the charge in April 1567, and the following month he married Mary. Following an uprising against the couple, Mary was imprisoned in Loch Leven Castle. On 24 July 1567, she was forced to abdicate in favor of James VI, her one-year-old son by Darnley. Wikipedia
(most of the stuff I've read indicates that her marriage to Bothwell was not voluntary; she was kidnapped and raped).
Boadica may qualify
Boudica's husband, Prasutagus, ruled as a nominally independent ally of Rome and left his kingdom jointly to his daughters and the Roman emperor in his will. However, when he died, his will was ignored, and the kingdom was annexed. According to Tacitus, Boudica was flogged and her daughters raped.4
And arguably Anne Neville
More important, he married Warwick’s youngest daughter, Anne Neville, widow of Edward of Lancaster. There is no need to suppose that this was a love match, for he insisted on her share of her parents’ immense inheritances in a bitter dispute with his brother George, husband of the elder daughter. The three royal brothers colluded in depriving the countess of Warwick of her entitlements, more than half of the whole.
My professional historian girlfriend suggests (somewhat tongue in cheek) Patty Hearst - because in America "princess" is a loose term. I've lost track of the number of teachers who argue that "celebrity" is equivalent to "nobility" at a minimum.
Slightly less tongue in cheek, I'd challenge the question; take for example Caroline of Brunswick, who was shipped off to a foreign land to marry a Prince. The decision was made against her will (arguably; she'd never met the man). Most royal women were the instruments of foreign policy, not participants. Kidnapped princesses were the norm, not the exception.
I just re-read the question and noticed that OP is looking for a military operation to seize a princess. I'd argue that Boadica still applies - the Roman's invaded the Isceni lands to seize the women. Mary Queen of Scots should still qualify - although technically it can't be a "military" operation, since both Bothwell and Mary employed Scottish troops. I'd argue that in most cases in both history and fiction, a military operation to seize a person is rare - a covert op is much more plausible. If you're going to exclude cover ops and police operations, then the question becomes artificially narrow.