First, thanks for reading, and the thoughtful questions
(A) What is France doing?
(B) It's one thing to conclude (as you evidently have) that Britain would have lost a Trent war had it come to pass. It's quite another to conclude that the British themselves believed that.
(C) In regard to your ultimatum:.
Answers to A, B, and C:
A. Napoleon III is pursuing his own interests; at the moment, that includes blockading Veracruz under the terms of the Convention of London, making encouraging noises toward the British and the Confederacy, and thinking deeply about his future, including about the fact the French have troops spread from China to the Papal States and that he needs the support of Catholics, in France and elsewhere; whether his interests are the same as those of France remains to be seen.
B. Opinion was divided in Britain, both generally and specifically within the Palmerston Cabinet; there was an English historian named Kenneth Bourne who spent quite a bit of time looking into what amounted to the proceedings of the ad hoc British war cabinet in the winter of 1861-62, including original research in the papers of everyone from Palmerston to Cornewall-Lewis to Somerset (Seymour) to Stanley, in fact; he published a monograph in 1961 (which I have posted in the past) and followed it up with a book a few years later. Basically, although there was a general feeling the RN could in fact both break the blockade of the rebel ports and impose one on the US Atlantic seaboard, the realities of a land war in the Americas were not any different in 1861 then they had been in 1815 or 1781, and were recognized as such.
Amanda Foreman's "
A World on Fire" came out a few years ago and, not surprisingly, includes a pretty extensive discussion of the
Trent Affair; what I have written here draws on Foreman and Bourne and one more author who has yet to be included; given that he was a contemporaneous source who knew of what he wrote, I think that should be reasonably convincing no thoughtful Briton was sanguine about an Anglo-American war in North America at this point. He will show up in the next chapter.
As far as Stanley's "opinion" goes, it is based on the cited sources, his liberalism, and the circumstances of his sons' lives in this period; seemed too good to pass up. Be aware that the eccentricities of the Stanleys are "real"; the 3rd baron did, in fact, become a Muslim and commit to a bigamous marriage with a Spanish Catholic; another son became a Catholic clergyman. Capt. Stanley is one of two (the other being the younger son, who also made it to America in this era) who promises to be a suitable heir. If it sounds too much to believe, they were, in fact, ancestors of the Mitfords...
C. Well, it's not war
yet; but the Lincoln Cabinet's vote to say no to the British note (by saying "yes" to something yet to be revealed) is a promise to meet force with force, essentially; given the British support for the rebellion in 1861 (despite the public statements regarding neutrality) anything less is surrender.
The fifth (fictional) point is essentially what the British and French asked for in the Black Sea after Sinope, which is what led (immediately) to war with the Russians in 1854, and in terms of being a short of war measure, somewhat similar to what the Convention of London demanded of the Mexicans in 1860; it struck me as the sort of half step someone of Palmerston's age, temperment, and position would have felt appropriate in this "bloodier" confrontation, yet falls short of an outright declaration of war.
Yet from the US position, it amounts to the US accepting British "guardianship" of the blockade, which is tantamount to opening the rebel ports and outright British government suppport for the Confederacy. I can't see the US accepting it, or the British accepting something similar, any more than the Russians or Mexicans did historically, or - for that matter - the Chileans and Peruvians accepting it from the Spanish later in the decade.
Best,