How about if McClellan loses the Battle of Antietam. The British and the French decide to step in and recognize the CSA and try to pressure Lincoln to stop the war. Lincoln refuses and the two European nations declare war on the United States. In retaliation the Union transfers what soldiers they had to spare to invade Canada and begin shipping a large quantity of troops to Mexico which the French are trying to control. The Mexican rebels kill Maximillian in 1864. His family in the Austro-Hungarian Empire then declare war on the United States in retaliation.
Prussia sees this as a golden oppurtunity to break up the German Confederation completely and declare war on Austria. To support their "Allies" France and Britain declare war on Prussia. Russia looks to gain territory from Austria and take the Crimean Penninsula from the Ottomans while Britain and France are distracted.
This leads to the entry of the Ottoman Empire. Spain looking to gain Gibralter and fearing that the CSA will take Gibralter joins on the side of the United States.
Prussia defeats Austria quickly and then turns its forces toward France. France with a war on their eastern border brewing abandones the war against the USA to fight Prussia. In addition Italy seeks to gain Corsica and so they declare war on France. By 1865 France descends into Civil War with the death of Napoleon III. Austria and France are now knocked out of the war. Russia easily overruns the Crimean Penninsula and the Ottamans are distracted by further independence movements closer to home so they leave the war.
Now the only people left in war that will fight in continuation are Prussia, the USA, the CSA, Britain, Spain and Mexico.
In Mexico the Imperial government is completely destroyed by 1865 so the Mexicans begin raids into Texas. Prussia negotiates a ceasefire with Britain in 1866. Spain has taken Gibralter from the British who are more concerned with defending Canada which the USA invaded in 1865. Lee occupies Baltimore but is bloodily repelled from Pennsylvania by Grant.
In late 1867 the Army of the Potomac under General Sherman takes Richmond. General Lee negotiates a ceasfire in 1868 and the American Civil War is over.
General Grant meanwhile has defeated the British repeatedly in Quebec and the British give up to defend the rest of the Empire which is revolting after the string of British defeats. Quebec is given independence. The United States takes the rest of Canada. In addition the British agree to abandon plans for the Sandwich Islands in exchange for total immunity over any war with Spain. From 1868-1872 the British seize Spanish colonies from Cuba to the Philippines and also take Spanish Morrocco and retake Gibralter.
Union wins. Britain loses Canada but gains most of the Spanish Empire. Germany is united. Austria has built up a hatred for Germany.
Anyone sense another war coming?