You can use the contextmenu event to detect right clicks as described in the earlier answer. Another way to detect clicks for the right mouse button is jquery's event.which:
clickTree: function(e) {
  if (event.which === 3) {
    // handle right clicks
    this.showtreemenu(e);
    return;
  }
  // handle left clicks
  this.toggletree(e);
}
For long clicks, aka measuring click duration, use mouseup and mousedown:
events: {
  'mousedown .measure-click-duration': 'clickStarted',
  'mouseup .measure-click-duration': 'clickEnded'
},
clickStarted: function(e) {
  this.clickStartTime = e.timeStamp;
},
clickEnded: function(e) {
  var clickDuration = e.timeStamp - this.clickStarted;
  if (clickDuration > 1000) {
    this.longClick(e);
  }
}
I made a fiddle demonstrating contextmenu for right clicks and the click duration described above.