If your goal is to cause the American Civil War to provoke a wider diplomatic crisis -- or, perhaps, even a wider war -- figuring out how to junction and combine it with the January Uprising is not a bad way to do it. I've brainstormed it as a plot device, and something like this is where I tend to end-up:
1) An alternative Pennsylvania campaign lets the Roebuck Motion escape Parliamentary purgatory and mediation is teed-up squarely before Palmerston's government;
2) Initial overtures are made to Austria, Prussia, and Russia about joining France and Britain in making such an overture; Austria and Prussia have no interest, but Russia is moved to do so primarily as a means of watering down the proposed terms of mediation.
3) An offer of Anglo-Franco-Russian mediation is made to the combatants in the ACW; the South obviously accepts and the Lincoln administration, after some internal thought, will accept mediation as soon as Russia submits the question of Polish sovereignty to international mediation, as the situation with the Confederacy is not different in its Big Picture substance.
4) Poison pill submitted, things should end, but for Otto von Bismarck being himself. Bismarck connives to alienate Austria from its (potential) allies in the West by trying to engineer a mediation of the Polish Question while remaining within the confines of the Alvensleben Convention by guaranteeing a united front with Russia in favor of a hard-line against the January Uprising. Being Otto von Bismarck and thus possessing a combination of skill and luck that borderlines on handwavery, he is able to convince the Russians to go along with this.
5) With the Russians on-board, Bismarck then connives to engineer an offer of mediation from Britain and Austria; the former because mediation checks off several of its strategic wants and the latter because the Austrians are the most likely to favor a hard line against the Poles (and because such will drive a serious wedge between Austria and France).
6) Bismarck's wheels-within-wheels machinations come to fruition and an Austro-British offer of mediation of the Polish Question is made, which is promptly accepted by Prussia and reluctantly by Russia.
7) The Lincoln administration, confronted by the supremely low probability event of the Russians actually submitting the January Uprising to mediation, must make a choice on the still-outstanding offer of Anglo-Franco-Russian mediation.
8) ???
9) Profit! (And maybe an independent Confederacy.)
But yeah, if your goal is to junction the two conflicts, good luck with that. It's going to be insanely detail-intensive and will, in any event, be insanely low-probability that relies heavily upon fortuitous strings of events and other almost-handwavery.