Before we talk about Emma, Horatio, and William we have to talk about Emma. Emma Lyon, or Emma Hart, was born to an impoverished family Cheshire - she received no formal education, and was alone and working in London from as young as 12. Initially as a servant, and then as an actress, model, and prostitute. We don't know when her sexual exploitation started, but it was formalised as young as 15. At 15 she was hired Sir Harry Fetherstonhaugh as a mistress and 'hostess' to entertain his male guests at his manor, he cast her out after getting her pregnant.

Her next protector/abuser was Charles Greville, who agreed to provide her with accommodation so long as she remained his mistress, gave up her child (also called Emma), and followed a strict set of rules. Still a child herself, she had little choice but to agree. Greville was not as wealthy as Fetherstonhaugh, and would eventually hire Emma out as a model for Sir Charles Romney - who produced many well known portraits of her. This helped her to become nationally known as a famous beauty. She received no income from this, Greville had complete control over her.

Greville eventually sought to marry a wealthy heiress but couldn't do so with a famous mistress, so he sought to pawn her off to his uncle - Sir William Hamilton in distant-enough Naples. It's not clear if Greville expected her back once his marriage was cemented, or if money changed hands, but the upshot is that Emma was sent to Naples not even knowing she'd been bought and sold. She thought she was going on holiday.

Now 22, and still having had little education (Greville taught her to mimic an upper class accent and required her to meticulously track all her spending, which improved her diction and maths but did not provide her with an education) she arrived in Naples.

Sir William was twice her age, widowed, and a major player in Mediterranean politics - as the British envoy to Naples. He was also a collector, collecting antiquities and art. He hosted many guests for the express purpose of showcasing his collections, and soon had Emma trained as a hostess to act as a part of the collection and its presenter. It was at this time that she developed her 'Attitudes' - a performance art where she would evoke specific emotions from classical theatre.

I lay all this out so that when we get to William and Emma's wedding in 1791 it's clear that this is not a typical aristocratic marriage. Emma would be presented to court (of the Kingdom of the Two Sicilies), where she would befriend the queen, and make many important connections. She also learned Italian, Neapolitan, German, French, and possibly some Latin and Greek, and completed her education. Sir William refused Greville's suggestion that he take in Emma's daughter (Greville had continued to pay for her upkeep, to the standard of a mistresses daughter, not a wife's.)

She became a celebrity - receiving invitations and job offers from theatres all over Europe, and even delivering letters to Marie Antoinette (sister of Emma's new BFF the Queen of Naples.) Emma Hamilton was a stop on the Grand Tour - wealthy British men touring Europe to see the beauty of civilisation would stop in Naples to see all of Sir William's collection, including Emma. You could buy prints of her likeness in London.

So enter Horatio Nelson. Also a celebrity. Also married. And also not an aristocrat. Emma initially helped him as a politic ally, brokering a deal to have the Neapolitan crown supply Nelson's fleet. After Naples fell to Napoleon, she persuaded Nelson to evacuate the Royal family. She had become a power broker in her own right. Nelson was catapulted to even greater fame when he used those supplies to push the French fleet out of the Mediterranean with the crushing victory at the Nile. This would also make him quite wealthy.

Horatio and Emma effectively lived as husband and wife. With Nelson's wife, Frances, forgotten about, and Emma's husband... Just sort of there. The press made huge fun of him, and his family observed it as a strange doting on Emma. Sir William at one point even wrote a letter to Horatio reassuring him that Emma was faithful to him, after the Prince of Wales's (effectively one of the richest and most powerful people on the planet at the time) attraction to her became public knowledge.

Now - Merton Place. Emma may have brokered the sale, but Horatio paid for it. It was never the Hamiltons' property. Emma became a part of the Nelson family, caring for Horatio's father, sisters, and nieces and nephews. She also had two daughters with Horatio (Emma and Horatia), one of whom survived childhood. Sir William continued as a family friend... Odd uncle... Husband... Until his death. Horatio would die not long after at the Battle of Trafalgar. Emma received nothing and died a tragic and sad death in exile and poverty some years later.

The odd threesome were fascinating to the British public, as they are to us. But Sir William had no power at Merton, and anyway supported their relationship. Notably, Horatio was the first man not to buy Emma. Indeed, she was the power broker in their relationship - at least early on. They're all very complicated figures, and Emma's lifetime of exploitation and objectification is truly tragic.

Edit: for a bit of context, it wasn't the sex that made them unique. What bewildered the public was the William, Horatio, and Emma all seemed to actually care about each other. William wrote Horatio letters of encouragement, Emma nursed them both when sick, Horatio hosted William in his house. That was not usual.