Here is an Ngram chart of "caved to" (blue line) versus "caved in to" (red line) for the years 1800–2005:
The most surprising thing to me is how recently "caved in to" took off in popularity (around 1960). The allied expression "caved to" has enjoyed its own upsurge in usage (starting around 1995), but it remains far les common than "caved in to."
As for the idiomatic meaning of the phrase, it is identical in both versions: to have one's opposition to something collapse, as if it were an underground tunnel dug through soft dirt or unstable rock. Here is one example from each form of the phrase. From "The Journey of Maryam Mursal," in [The New Crisis] (July 1998):
Eventually, Barre caved to political pressure and lifted the ban on her music, even giving her a house as compensation. However, instead of the obsequious appreciation he expected, Barre met a proud and defiant Mursal.
And from Gerald Graff, "Self-Interview," in Confessions of the Critics (1996):
A recent case in point is the celebrated battle over the "Cultures, Ideas, and Values" requirement at Stanford [University], which was "resolved" by creating eparate course-tracks for traditionalists and revisionists so that no communication nee take place between the two. When Stanford revised the requirement it was widely reviled by conservatives like William J. Bennett for caving in to pressure from multiculturalists and other insurgent groups. But if Stanford "caved in" to pressure, it caved in to pressure from all the factions involved, including the conservatives.