That´s not how the Spanish dealt with migration though, and there is a limit on how much they can enforce.
The Spanish didn't allow non-Spanish immigration until the late 1700s, and even when they did, it was pretty slow until the Americas rebelled and formed their own nations. It doesn't seem too far out that the Spanish would neither need to, nor want to provide blanqueamiento incentives to European immigrants. Since criollos are rebellious, and the Spanish would keep slavery longer than the independent republics did (meaning the price of labor is low, deterring immigration), they don't necessarily want non-Spaniards to immigrate to the colonies.
Also if Spain dominates the economy of Latin America instead of France and Britain dominating Latin America, then Spain will be able to feed its growing industrializing population in the 19th century., and maybe prevent some of the civil wars So there may be more Spaniards ITTL, meaning more peninsular settlers to fill up Latin America, pushing even more of the non-Spanish Europeans to the US and Canada. The additional Spaniards may settle in the United States, as well.
I can see non catholic immigration not being a thing, but that would still leave a lot of room. European cold live there and they did, from Argentina to Colombia, European immigrated pretty much everywhere.
Because of intentional promotion of European immigration, and also because slavery was abolished in most Latin American countries earlier than the US (except in Brazil) meaning cheap labor from Europe was needed. Neither will be the case in a surviving, semi-reactionary Spanish Empire.
Only in Argentina, Uruguay, and Chile would you see European immigration happen anyway, because those climates are temperate and suitable for European farming. In Colombia, Ecuador, Peru, Brazil, Paraguay, Venezuela, and Central America, European immigration was only suitable in very small regions along rivers and mountains, which can easily be filled up by Spaniards and Italians.
But the USA-Britain relation were too economical interdependent to become hostile, if they are hostile immigration is going to be less a thing given the USA could be potentially a less isolationistic and more militarized.
Well, the US can always trade with Germany, a more populous France, the Spanish Empire, Russia, Japan, China, etc. There are plenty of agricultural and industrial nations to trade with, even while trade with Britain is temporarily limited.
And the US had huge tariffs on manufactured goods from 1783-1945. So a war with Britain in the 1890s, especially if the US already had the good parts of Ontario, would only cause a temporary recession.
Militarized? No reason for it to last longer than the war itself. Even if it does though, military buildup, at least before the last third of the 20th century, is a significant injection into the economy. In the late 19th century, such buildup would be largely naval and unimposing on the nation as a whole.
True, but I´d argue that without any super big war you would more overall immigration, maybe with economic decline and some minor civil wars or border wars.
That's a valid idea as well, although if some of the countries in Europe are still prosperous, then 20th century Europeans will simply migrate to other European countries, rather than to America. If the US population is to be maximized, the whole European continent has to be weakened. (Rather macchiavellian, but it's the scenario at hand.)