For all your mouse actions, you need to check also the mouseX,mouseY coordinates (whether they are in the left or in the right segment), and then choose the action accordingly (drawing or switching the tool). There are some GUI libraries available for Processing ( http://www.processing.org/reference/libraries/#interface). 

Depending on how many buttons you have and how closely they are arranged, another option is to provide the whole workspace for drawing, but overlay it with a semitransparent layer that contains the buttons. If the user clicks a button, the action is performed, otherwise if he clicks, moves are draws beneath the buttons, the drawing or dragging action is carried out. See  http://www.infochembio.ethz.ch/rauminformation.html as an example (zoom map using slider to say 2, then click besides the slider and other buttons to drag the map). Source code available at  http://www.infochembio.ethz.ch/rauminformation_about.html . Have a look at the two modules (PDE tabs) library_space_navigation.pde and library_space_events.pde.