History is filled with decisions by world leaders that would be considered ASB in an ATL. Hell, the entire lead up to WWII was pretty much one ASB level stupid decision after another.
Get the Mexicans to seriously misjudge the Americans, maybe they assume that Wilson doesn't have the balls to commit to an officially declared war, have them assume that the Germans are very likely to win the war(throw in an extra naval victory in there, perhaps a much better showing at Jutland for instance), and have the Germans be very good salesmen to the Mexicans. With those ingredients, you could get Mexico to start something really full scale. Lord knows that the Mexicans had plenty of reason to despise the American Government.
Pretty much, what went down during the Revolution would have actually been a perfectly acceptable reason for the Mexicans to declare war, though cooler heads likely prevailed when they realized that they would never win a war with the USA.
But anyway given this eventuality you've concocted...
The Germans would be more confident in their position now that they've had a couple of victories against quite possibly the biggest threat they face in the war. This might mean that they actually do back up Mexico with weapons and funding, absolute best of the best case scenario, a very small expeditionary force.
A war with Mexico around the Huerta-Carranza timeframe is going to speed up two things for the USA.
1. War with Germany
2. Mobilization and expansion of the American military.
Wilson's strategy for Mexico is probably going to involve a quick victory that bloodies Mexico's nose and certainly involves a regime change. Wilson was perfectly willing to overthrow regimes he felt were troublesome and Carranza is going to forfeit his trust with Wilson.
However now that I look more at the issue I am leaning towards supporting a more aggressive version of the Tampico Affair. Carranza was very friendly to Wilson and the USA in general and it was under his tenure that Mexico vetoed Germany's supplications of Mexico for a war with the USA. His predecessor Huerta was held in much lower esteem by Wilson, and it's not hard to imagine that that German vessel bound for Veracruz full of arms shipments might have been turned into a very small expeditionary force or one of advisors for the Mexican military if Germany was in a better position in World War One.
Ipso facto, Wilson tells the rest of the Latin American nations that offered mediation to go shove it and goes to war with Mexico with the end goal of ending Huerta's rule over the country (possibly installing Carranza) and quite possibly nabbing Baja. Wilson's going to impose a light peace though, he isn't going to make his own supported ally accept a harsh, taxing peace for the war, especially in light of the consideration that he's about to go pay the Germans back for the war as well.
However this Mexican-American War will not be the only major event this timeline covers. World War One is easily still going to be something the US is involved in, and I think it will still largely end the same way. Germany's alterate timeline victories at sea will be rolled back, perhaps by a liberal application of American naval force combined with the British Royal Navy to undo all of Germany's work and restore the blockade to its full extent.
Whether our peace conference goes the same way, well I don't think a better-performing Germany that's been defeated is liable to be any more well-received by the European powers, but overall little change to the terms imposed and who wants what, we've affected the course of the war but largely achieved the same results and the same nations and leaders are still in the game. I can see this going very badly for Wilson's goals or very well, depending entirely on how he handles it.
That public sentiment will rage against the Germans more so than OTL is almost guaranteed with a Mexican-American War. However, I cannot see Wilson not still fighting hard for the League of Nations. I guess my query is this: if Lodge and all the other hawkish Republicans got exactly what they wanted from a successful war with Mexico and then Germany straight after, will they be more amenable to allowing Wilson to have his League of Nations albeit with perhaps some compromise on certain aspects of it that they feel limit the USA's sovereignty?