Would I not need to send a boolean as well as the potentiometer values for the button's state?
Sure. I forgot about that requirement.
I just don't know how to map those values to the potentiometer values in the serialEvent() method.
I don't understand what mapping you are talking about. You are sending x and y (and adding the switch state) from the Arduino, as strings. The serialEvent class captures the string, and extracts the values as floats (why, when they are sent as ints, excapes me). Just assign those floats (or, better yet, ints) to posX and posY.
You may need to scale the data from the Arduino to match the screen size, but that is a simple matter.