The solution is quite simple, really. By repairing the Commonwealth, we will ensure Britain that they are indeed a good friend of America's, one we won't so easily cast aside as some would want us to. The Commonwealth is, if nothing else, the reassurance of our commitment to establish a long lasting and friendly relation with Britain. I say this not to shy away from the Triple Alliance, but our relation with Britain is special to the point of being ingrained in our very history. I see no reason why we cannot look towards the Triple Alliance while we are patching the Anglo-American relations. If anything, I view this move will be seen as a thawing of tensions. Having the great United States approaching Triple Alliance, looking for trade and diplomacy, might motivate and inspire these nations of the ideal of American Exceptionalism, the astounding and vast idea of Equality under the law, under one nation - that we, a friend of Britain, will not rebuke these nations because of the shared animosity in Europe, but in fact, that we are acting in our own regard, forging the path of righteousness. It has been stubborn grudges and past wrongdoings that have caused countless European Wars. America is not interested in that, we are far above that. By establishing ties with all of Europe, they can truly see the beauty of the American way.
Now, the pressing issue you have set forth, of the United States view of the important of the Americas versus Asia, Africa, and the rest of the colonized world. This should be quite simple. I look to it as an issue of proximity. I am more ready to defend the United States, by using our great Military, against nations that could pose an immediate threat to us. On that same now, I prefer to establish long-lasting relations and friendly dialogue with those nations whom we share a continent with because of our location, and the idea that a local friend is better than a far away friend. It is simply more simple and practicable to support those closest to us, for the sake of maintaining relations, trade, and all other aspects of governmental affairs.
As for your last question, yes. I would have to agree that any military intervention at all, would be most best used inside Latin America. I would like to make it clear that I have no grudge against Latin America, nor do I wish to send our military roaming the Earth like a bunch of bandits. I would use this as a tool of last resort, simply for the reason I outlined above why I favor the befriending and influencing of American nations. I'd much rather have diplomatic ties broken off with, lets say, a small Asian nation than Chile. Its effects would be immediate and seen instantly.