long journey from Hampshire
The counties of Hampshire and Surrey (the location of fictional Sanditon) are next to each other, meaning the journey was likely no more than 50 or 60 miles. Although this was no inconsiderable distance, Diana is likely exaggerating the fatigue of traveling between two adjacent counties.
who would have been nothing at Brighton
Brighton, located along the coast of Sussex, grew considerably as a popular resort town during the early nineteenth century. From 1769 to 1818, its population grew from 3,000 to 18,000 people. Brighton was a fashionable holiday destination, frequented by members of the British Royal Family.
https://janeaustensworld.wordpress.com/2007/06/25/brighton-a-popular-seaside-resort/
six new dresses each for a three-days visit
During the Regency period, it was common (and expected) for women to change dresses multiple times per day, depending on the occasion. A morning dress (worn until dinner), walking/promenade dress (worn on walks and during shopping), and an evening gown were necessary wardrobe staples.
tonic pills
At the end of the 18th century, tonic pills were believed to be an effective form of dieting. After the extravagance of the Georgian period (especially George IV), it became fashionable and responsible to lose weight during the Regency period.
any complaint which asses' milk could possibly relieve
Donkey milk was considered a viable medical treatment from antiquity (Cleopatra bathed in it) until the turn of the 19th century, when it largely went out of fashion. It was considered a generic cure for a variety of conditions, including gout, scurvy, coughs, colds and asthma. For many, donkey milk caused stomach problems and "lactose intolerance."