How come my switch is triggering with out pushing the button?
I want the relay to trigger and stay open only while the button is
  pressed. However for some reason touching pin 2 triggers the relay and
  sound, even if I'm not connecting it to the ground.


Touching a pin is like connecting it to ground with a resistor (human body is conductive). It may or may not be stronger then the pull-up resistor.


  If i remove the tone (speaker, 100, 300); it only triggers when the
  button connecting pin 2 to ground is pressed, but obviously doesn't
  play the tone.


Activation of the neighbor pin influences the pull-up on pin 2. Try external pull-up on pin 2.