Yeah, rather OTL except their social scene; Leopold was domestic and he and Charlotte spent most of their short married life at Claremont in country, domestic bliss. Here we have them with a court of their own in London and part of Regency society. Charlotte's first pregnancy involved a collapse at the opera and was a miscarriage. Here it was at a soirée, and is just the beginning of her pregnancy (well, that they know: like poor Victoria, she conceived not long
after her marriage, probably c. December 1815). Friedrich only had two kids IOTL though, so I don't think Charlotte will have to worry of constant pregnancy. It depends on how good of a "match" they are.
As for Prussia, the King of Prussia is quite pleased with the marriage and hoping he may benefit diplomatically from it. Friedrich had some properties IOTL in Germany, mostly due his military career; here he may still have
Schonhausen Palace as Friedrich grew up there in his youth and it wasn't used by the reigning Hohenzollerns. I can see them visiting, but not sure about living there. Friedrich's minor in the Prussian succession and Charlotte didn't want to leave England. I can imagine them taking a grand tour, or perhaps some scandal forcing them to live abroad. Maybe in the 1820s, George IV gets fed up with her popularity and maybe meddling (perhaps she supports her mother over him), and he makes her leave the country?