They can very easily make the case that the Union was attacked in both cases...
Most certainly. The Democrats are wheedling the Republicans in certain cases, and it is about the war, but hardly for peace. IIRC during the Trent Crisis in OTL many Democrats berated Lincoln for backing down, even Clement Valladingham that arch Copperhead. He and his fellows are still causing trouble, but I'll cover how its a touch different in an upcoming chapter.
Remember the Confederates opened hostilities by shooting first at Fort Sumter. The war, call for volunteers, further secession and massive response of volunteers (on both sides) all stems from the fact that South Carolina opened fire on a US Army post.
As to the British, it is an easy matter to claim that the British started the shooting. TTL, a raid by Confederate soldiers using Canada as a base into US territory while the Trent Affair is arguable (that argument basically starting the war after all) but the Terror / Dacotach affair is very easily spun as an uprovoked destruction of an American naval vessel attempting to operate within the standard rules. The high American death toll makes that very easy indeed.
The first two instances could be easily argued back and forth by both sides, and perhaps some sort of diplomatic recompense might have been reached had time been allowed for tempers to cool, but
Dacotah-
Terror made that impossible. Even the Canadians bear some responsibility for the spectacularly ill advised release of the raiders (even if that was just a local magistrate screwing up) which Macdonald acknowledged. However, the government in London bears just as much for the completely inflexible orders given to their diplomatic and military personnel. Then of course, when the ultimatum did expire they definitely shot first (just like Han Solo) by marching across the border in Maine and seizing Houlton and Fort Fairfield in February even before the Battle of the Keyes.
While the British certainly have reasons for being belligerent, they've acted remarkably poorly in their handling of the crisis. It will have very...negative effects down the line.
Fucking South Carolina, always ruining shit for everyone else.
Could work, in theory, if this had been a spur deal. Issue is, it's been building for some time.....
And I guarantee you they're gonna
keep ruining things too. What's that old quote? Too small for a Republic, too big for a lunatic asylum?
The Anglo-American relations of TTL will not be quite so rosy after the 1860s here that is guaranteed, and both sides are either going to try to dictate peace at the point of a sword, or bow to reality from sheer exhaustion.