Traversing the Horn from the Atlantic to the Pacific was difficult but not impossible, and was done often enough so as not to be all that unusual. One particularly good account is the travels of HMS Doris, a frigate that would be somewhat similar to Bacchante, in the 1820s. During the mid-1700s, Anson made a stunningly successful voyage around the world, sailing from East to West around the Horn ( voyages that Anson made). Clipper ships did make this voyage quite frequently during the California gold rush (1849+), taking passengers from the US East Coast around the Horn to the City. That's not to say that it is easy, as many ships found it to be a maddening and storm tossed experience.
As far as friendly ports, they will have ports available to them in Brazil, as that is a Portuguese colony. The Falkland Islands would have been largely uninhabited, but could have made for a quick stopping point if necessary, although probably only for water.