I was listening to Hamilton and King George was in charge of almost everything, the military, taxes, everything. At what point did that stop happening? As of now, the royal family has almost no affiliation with British politics, they have a prime minister, senators and things like that. Did they have them back in the 1700s - 1900s?
There's a section on the British Monarchy in the FAQ. In particular, the first answer by /u/Hollack seems to address your question directly.
EDIT: This answer also in the FAQ by /u/Three_Trees also directly addresses the question.