If you're doing this quest near reset (like 3am EST or something) watch out for the fact that the days of the week very well may change. I was doing it late one night and I went from Tuesday to Monday once we hit reset.
ask butler lady
ask doctor introduction (mellieu)
buy pills (london nurse)
give pills doctor (be sure to wait for him to give the letter!)
go to butler
give letter butler
go to lady
ask lady high society
get rough leather pants from npd pirate (or the skirt from sabiha for females)
go to the tailor (or designer ss from the tailor)
ask tailor/designer ride
give pants tailor/skirt designer
go to stables on wednesday 2pm
wear jodhpurs (a pair of tailored leather jodhpurs, a long riding skirt for females)
ask master horse
ride horse
ask lady ride
follow lady
ask tailor/designer ball
give tailor bolt of silk (buy from cassim, agrabah)
give tailor string of emeralds (oonagh)
wait one day
go to tailor/designer
go to mansion saturday night
wear pin (choker if female)
wear tuxedo (gown if female)
go to ballroom