While the show is fiction inspired by history, King George did actually say in a letter, "I am born for the happiness or misery of a great nation, and consequently must often act contrary to my passions." However, this sentiment was written before he met Queen Charlotte. At that time, he wanted to marry Lady Sarah Lennox but was advised against the marriage by Lord Bute.
In the finale, Queen Charlotte learns that Prince Edward's wife is with child. They moved to Germany shortly after their marriage and returned to England only one month before the birth. This child would be the future Queen Victoria. Prince William and Princess Adelaide were also expecting a child at around this time, but all of their children were stillborn or died within a few months.
Less than a year after the marriage, on 12 August 1762, the Queen gave birth to her first child, George, Prince of Wales. Almost exactly a year later she gave birth to her second child, Prince Frederick on 16 August 1763. In total, between 1762 and 1783, she had 15 children, 2 of whom died during their childhood.
Prince Edward and his wife are played by actors close in age and look to be in their mid to late 20s. In real life there was almost a 20 year age difference between the two and Edward was just over 50 when the future Queen Victoria was born.
King George and Queen Charlotte dance to a classical rendition of SZA's "Nobody Gets Me" at the ball.