Not strictly an update - more of a test of a different writing style...
"You can't be suggesting that we give up on this! These... these... rebels have been captured by the Federal Government, and-"
"It is not the question of whether they are rebels which exercises me, Mr. Stanton-"
"Gentlemen," Lincoln said firmly.
The talk subsided, and all eyes turned to the tall man who was the President of the United States.
"Gentlemen, we have been about this for two days already," Lincoln stressed. "We have talked for all of Christmas Eve, and all of Christmas Day, and now we look fair to talk through all of Boxing Day as well. But the time we have for talk is not unlimited."
He left a pause, for anyone who wished to speak up, then continued. "Mr. Welles, the facts of the incident please."
"The facts, Mr. President," Welles confirmed. "On the 8th of November last, the sloop San Jacinto - under Captain Charles Wilkes - intercepted the British mail steamer the Trent in the channels between the Bahama banks and the island of Cuba. There he stopped the Trent and took off the persons Mason, Sliddell, and their secretaries, charging them to be contraband."
"So much for the facts of the incident," Lincoln agreed. "Mr. Seward, what of the response?"
"I have been informed by Lord Lyons that the action of Captain Wilkes has been seen as illegal by the British Government," Seward stated without preamble. "Lord Lyons is the British ambassador to the Union, as you all know of course, and he made this case to me earlier this week in forceful terms - it is clear to me that he is acting with the instructions of the British Cabinet. I have been shown his covering letter, for he had permission to do so, and it is clear that anything short of capitulation - of surrendering the aforementioned commissioners and their secretaries - would be grounds for Lord Lyons to immediately depart this country, and would mean war."
There was a moment of hushed silence, for this was a part of the response they had not heard yet.
"I cannot bring myself to believe that the British would give us only the options of capitulation or war," Lincoln stated. "We are well aware of the Rebel sympathies in some parts of the British government, perhaps, but I have been assured that the British position with regard to the Rebellion is to avow neutrality."
Seward began to speak, but subsided as Lincoln kept talking. "It is my opinion that the very harshness of the British dispatch is intended to ensure that we do not delay in announcing our official position."
"What position will that be?" asked the Secretary of War, Cameron. "There has been a great spirit of celebration throughout the land for the capture of the Rebel commissioners - I do not think we should lightly tell the country that it was all our mistake, and that the greatest and most admired victory of the War thus far must be abrogated."
Seward still looked uncomfortable.
"I have heard the opinions of a number of respected legal professors on the matter of the Trent," Bates spoke up. "From Theophilus Parsons of Boston to Richard Henry Dana and to the former Minister to Great Britain, Edward Everett, all are agreed that the seizure of the commissioners was a legal one."
"My thanks, gentlemen," Lincoln nodded. "I believe that this confirms my appreciation of the situation."
He nodded to Seward. "Mr. Seward. Please inform Lord Lyons that, on this issue, we feel that it is of the utmost importance to seek the best resolution for all concerned that comports with international law. As such, the persons of Mason and Sliddell will not be released, though we would not oppose any attempt at international mediation which the British Empire wished to organize, pursuant to a mutually agreeable selection of mediators which does not unduly bias the deliberations of the panel."
If I went with "book-izing" this TL (in the course of which I'd correct a few things, probably have more of a Montreal Offensive, and definitely change the West Coast!) then I'd probably start here, or rather anything before this would be OTL sources or very similar.