Yes, she is the princess I was thinking of- although maybe in a version of the painting other than what you posted. Vigee Lebrun did several portraits of members of the Neapolitan Royal family when she visited Naples in 1790 and it is easy to confuse them.
I am sorry the year Lady Mary Coke visited Vienna came out as 170. I am trying to think of what year this was when she saw Maria Ludovica in Vienna- perhaps 1765 to 1766- within the first year of her marriage to Leopold? Sources I have access to note the birthplaces of ML's children from 1767 to 1788 as always being in Tuscany.
Also, I think the young Elector of Saxony, Frederick Augustus III, may not have yet been married in 1768, (or was he?) so did Maria Theresa describe ML in a letter to the Elector's mother, the widowed Electress of Elector Frederick Christian? And, I am wondering if MT felt she had to be very tactful considering the fact ML's mother had been the sister of Elector Frederick Christian and her own daughter Maria Christina was married to their younger brother Albert. Also, wasn't MT considering a third marriage for Joseph with Princess Kunigunde, the youngest sister of this family?
It is so interesting to have the recollections of persons such as Lady Mary Coke as resources with their observations of the lives of royalty in the 18th century.