Her article in thepeerage is here. Her husband Baron of Redesdale; her son became the first and last Earl of Redesdale.
Upgrade image with corrected date posted 3 April 2015 from liveinternet.ru/users/4851831/post318810164/.
Lady Frances wears a dress with a criss-cross bodice and loose fit, suggesting the early 1800s as a date for this Hoppner portrait. The placement of her collar suggests she may be wearing a vest or similar garment.