The biggest obstacle to this scenario is the ethnic make up of the American population.
Even as recently as 1917 the U.S. had such a large number of recent German emigrants that our entry into WWI on Britain’s behalf was not a certainty. Some of the Pennsylvania Dutch National Guard units that we sent to France for WWI spoke their dialect of German as their everyday language. The officers of these units found that they and their French counterparts could communicate more effectively if the Americans spoke their German dialect and the French spoke Hoch Deutsch. One American unit strayed behind the German lines and was about to fired on by the Germans until the Germans heard the Americans using their Pennsylvania Dutch.
Some of my ancestors came from the Rhineland as early as 1730 and eventually settled in NC. English was their everyday language by the time the Civil War started, but my grandmother remembered that her grandparents still used their German dialect in the 1920s and 1930s whenever they didn’t want the children to know what was being talked about.
I seriously doubt that the U.S. would have gone to war with Germany at any time during the 19th century.
The Germans were more of a minority in 1870 than they would be in 1917. There are certainly some States where they had significant populations, but they were not considered a hugely influential power bloc in the United States at that time. And a great many of the Germans who were in America in 1870 were either refugees from the revolutions of 1848, or children of refugees from the 1848 revolutions. These people will have little love for the Prussian monarchy and be quite likely to support a war which they see as a means to undermine it.
And, it might be pointed out, the ethnic makeup of the American population in 1812 was almost entirely British, yet we went to war with Britain to protect freedom of the seas, which is what is happening in 1870 in the timeline. Given the number of times we have gone to war...both officially and unofficially...over that very issue (1798 vs. France; early 1800s vs. Barbary Pirates; 1812 vs. Britain; even our 1917 entry into World War I vs. Germany can be counted as one of these), it is certainly not a stretch to imagine it happening again in 1870.