I'm not sure how you'd get a blowback to Europe.
1864-1866. The Chincha Islands war was a conflict between Spain and its former colonies, Peru and Chile, and a rather foolish attempt by Spain to reassert control over its former colonies. But it pretty much flopped on its own, and hardly amounted to all that much. The war seems to have been caused, in part by Queen Isabella's floundering attempts to regain Spanish influence in the former colonies and stature worldwide, there was also a war with Morocco. But Isabella was deposed in 1868 and abdicated in 1870.
1864-1870. War of the Triple Alliance. Brazil, Uruguay, Argentina vs Paraguay. Basically an Inland war. Could Spain get involved? The war started over meddling in Uruguayan politics, so.... possible? Isabella seems the sort to get disastrously in over her head, and potentially, if she saw an opportunity to take sides in Uruguayan politics... who knows.
Both the War of the Pacific and the War of the Confederation seem to be too far outside the time window to be relevant.
Ah but between 1860 and 1862, you have the Comic Opera 'Kingdom of Araucania', when a french explorer tried to unite the Mapuche of Patagonia to resist the expansion of Chile and Argentina.
Now, there's some interesting politics going on there. Chile actually got a long relatively well the the Indians, and at one point claimed the bulk of Patagonia. The Argentines not so well. Between 1870 and 1885, immediately following the war of the Pacific, the Argentines got very serious about conquering Patagonia. There were some tensions with Chile, by when Chile got into its 'War of the Pacific' with Bolivia, they settled out with Argentina.
Now, there's another Wild Card character in Europe, Napolean III. In OTL, he got heavily involved in Mexico around this time frame. Maybe it's not hard to imagine him throwing some weight and a few troops to the Kingdom of Auracania, which moves it from a joke into a bona fide country and possible protectorate. Assume Chile sides with Auracania, then this creates the spectre of a France/Auracania/Chile Axis.
How that would interact with a Chile/Peru vs Spain war. Or the Triple Alliance war, I don't know.
But with Spain and France meddling, you might see England getting involved, and there'd almost certainly be some blowback on the Prussian situation.
Anyway, that's my thinking. Again, if you think its got possibilities, go to it, do the research, and develop.