I don't think the Alcmene was at the Nile - but details here might fit with your story.
http://www.ageofnelson.org/MichaelPhill ... p?ref=0100it says - In December 1798 a rebellion in Naples allowed the French to enter and the Royal Family fled in NELSON's VANGUARD.
On the 20th. NELSON ordered three barges and the cutter of ALCMENE, armed with cutlasses only, to assist in the evacuation of Naples. Only one barge was to be at the wharf, the others to lay on their oars outside the rocks. The other boats from ALCMENE were to report to VANGUARD and, with 4 or 6 soldiers in each, row half way towards the Mola Figlio.
The ALCMENE was ordered to be ready to slip in the night if necessary. While VANGUARD took the Royal Family to Palermo on the 23rd., ALCMENE remained at Naples watching the Neapolitan ships of war. These were burnt in January 1799 by the Portuguese against NELSON's orders.
sorry, can't help with locating the portrait.
Cheers, MTS