I searched the internet for some material on Maria Carolina and found far too many items on Lady Hamilton.
Although Lady Hamilton's behaviour was rather on the kinky side i do not believe she had an affair with the Queen.
Far too many impossible , often gay or lesbian, relationships are ascribed to royals.
It all started with the first dynasty of Imperial Rome. The killings are often real, the orgies not.
For the Roman histories have been written down by aristocratic republicans, after the dynasty was extinct.
Again during the religious wars in 16th century France where almost every royal was accused of gross indecency.
Which gave rise to modern republicanism..
Even more with Queen Marie Antoinette who settled down in a rather bourgeois life.
I know the royal couple of Napels was not as close as that of France.
But you have to realise most royal males in those days were allowed affairs when their consorts were pregnant.
However, i do not believe a word about the lesbian affair as neither of the women ever was in another affair with their own sex..