Tricky. Here's how I'd do it:
• In 1785, rather than have his marriage to Mrs. Fitzherbert declared null and void, Prince George is disinherited and his younger brother Frederick made heir to George III.
• George is then given duties in the army. He cleans himself up and serves heroically in the Napoleonic Wars. Meanwhile, with the king's health failing, Frederick becomes Prince Regent.
• In 1819, George III dies a year early. The new King Frederick uses the unrest in Manchester and elsewhere as an excuse to crack down on Radicals, Whigs and the less fervent Tories. The people, and enough of the army, turn to George, their "rightful king," who overthrows his brother and becomes a reformist king.