So I'm not sure "switch sides" is the best phrase, since the US wasn't a proper belligerent, despite the occasional involvement, and more importantly, the Mexican Revolution saw a veritable parade of figures and factions in the ascendent, so American support of course depended greatly on who was seen to be in the US' best interests. While it doesn't cover the whole war, this piece I wrote about the 'Ten Tragic Days' will likely be of interest for you as it covers one period of US involvement and support - and a change in it.