I have to say that I disagree with you on one thing. I believe that the Brits definitely want the CSA to win their independence. It benefits them to weaken the United States and gain a potential ally in the Confederacy. So I disagree with the opinion that the British aren't fighting to aid the CSA in their independence. A war where the CSA ultimately still loses will be viewed as a loss for the British. Of course, this is all imo. Also, isn't Millard Fillmore the current NY governor? That's VERY cool and interesting.
The British wouldn't
mind the Confederacy winning, but the question is whether they are willing to expend the blood and treasure to guarantee their success. Palmerston is a decided no on that front, he simply wants to humiliate the North. There are powerful members of the War Cabinet (Russell, Gladstone, and Somerset) who are coming around to seeing that the South being independent might benefit Britain in the long term. Palmerston, like OTL, won't move on it for the moment as he's more concerned with the problem right in front of him.
If the Confederacy were to lose, it wouldn't be a major set back for British policy. Their world wide interests would be secure, they would have enforced a peace on their North American rival, and Canada would be secure for the moment. The Confederacy is an ally of convenience, a co-belligerent. They have as yet no reason to come closer together since their war aims are still different. The Confederacy would very much like to believe Britain will ensure their independence, but for the right price Britain would happily step away from the conflict.
And yes, Fillmore is indeed the Governor of NY, which will have some interesting connotations later on.
How do/will the average Northerner feel about the the South and Britain in this very bitter, esp. to Northern civilians, TTL War? And with active War propaganda to boot.
The average Northerner feels very angry towards Britain and the South, however, that anger is directed along party lines. War Democrats are generally supportive of the war to keep the Union whole, and were quite supportive of the war against Britain at first. Now though, they broadly agree with the emerging Peace Democrats that stopping the war with Britain is a necessity and going on fighting is a waste of time. Peace Democrats obviously want peace with the South and Britain, though they will argue (depending on the crowd) that the war with the South must be stopped so they can fight against Britain, but largely they want the armies to disband and peace to be signed.
Republicans are also split. Abolitionists think the fighting against Britain is pointless when the South needs to be fought, but are willing (through the Radicals) to support Lincoln for now as it serves their ends. Though whether they will stay the course with Lincoln depends very much on whether they continue to see success into 1863. The Emancipation Proclamation has them placated for now, but they will be wanting more. Republicans in general hate both Britain and the South and will support the war, but they are getting tired of it.
So much for both parties will depend on what happens in 1863...