Show us one scintilla of evidence in the history of the people in the US , especially those of that era, that would suggest in anyone’s wildest dreams, that the citizens would surrender?
This seems to be the core of your objection - the idea that the US would never contemplate any kind of negotiation without a total occupation.
This seems to me to be, frankly, unsustainable as a view unless one's viewpoint is thoroughly based on the idea of America as unique and exceptional - and it's also not fitting with actual US actions in wars of the past.
Take the War of 1812. In that war, the US did indeed negotiate, and it negotiated a treaty in which it recieved none of the things to which it had gone to war - it did not require a British conquest of every single state before the US would be willing to talk terms, it took blockade and land action (and even when the land action didn't exactly result in the British running the table the blockade was still sufficient to cause the US to come to the table).
In my view, the likely course of events is like this:
- Trent war kicks off
- The British establish a blockade, cut off supplies to the Union, and reinforce Canada
- The Union is unable to take Canada and is unable to break the blockade
- The blockade inflicts economic hardship on the Union, while the need to defend against various British attack vectors and the lack of European weapons going to the Union means that the Union's ability to fight the Confederacy is seriously compromised.
- A combination of the British exerting pressure on land in the north and the better-armed Confederacy causes Union reverses on land
- The Union's strategic material reserves (lead, gunpowder) drop rapidly, as do their number of troops as they can't replace their small arms
- A combination of the continuing blockade, an inability to see a route to end either war in the short term and the situation overall deteriorating with no way for it to improve (because of the continuing blockade badly damaging the Union economy, the army shrinking through casualties and weapon breakage, and the rapidly dwindling amount of critical war materials) leads to the Union deciding to cut their losses and sue for peace
This does not actually require British-Confederate cooperation, and despite this it's the most plausible scenario I can see for Confederate independence. It also doesn't require major British occupation of a large area of the US (though it does expose most every major US city to some kind of raid apart from maybe Pittsburgh).