Use the following code for reversing mouse clicks. 
$.extend($.ui.draggable.prototype, {
        _mouseInit: function () {
            var that = this;
            if (!this.options.mouseButton) {
                this.options.mouseButton = 1;
            }
            $.ui.mouse.prototype._mouseInit.apply(this, arguments);
            if (this.options.mouseButton === 3) {
                this.element.bind("contextmenu." + this.widgetName, function (event) {
                    if (true === $.data(event.target, that.widgetName + ".preventClickEvent")) {
                        $.removeData(event.target, that.widgetName + ".preventClickEvent");
                        event.stopImmediatePropagation();
                        return false;
                    }
                    event.preventDefault();
                    return false;
                });
            }
            this.started = false;
        },
        _mouseDown: function (event) {
            // we may have missed mouseup (out of window)
            (this._mouseStarted && this._mouseUp(event));
            this._mouseDownEvent = event;
            var that = this,
                btnIsLeft = (event.which === this.options.mouseButton),
                // event.target.nodeName works around a bug in IE 8 with
                // disabled inputs (#7620)
                elIsCancel = (typeof this.options.cancel === "string" && event.target.nodeName ? $(event.target).closest(this.options.cancel).length : false);
            if (!btnIsLeft || elIsCancel || !this._mouseCapture(event)) {
                return true;
            }
            this.mouseDelayMet = !this.options.delay;
            if (!this.mouseDelayMet) {
                this._mouseDelayTimer = setTimeout(function () {
                    that.mouseDelayMet = true;
                }, this.options.delay);
            }
            if (this._mouseDistanceMet(event) && this._mouseDelayMet(event)) {
                this._mouseStarted = (this._mouseStart(event) !== false);
                if (!this._mouseStarted) {
                    event.preventDefault();
                    return true;
                }
            }
            // Click event may never have fired (Gecko & Opera)
            if (true === $.data(event.target, this.widgetName + ".preventClickEvent")) {
                $.removeData(event.target, this.widgetName + ".preventClickEvent");
            }
            // these delegates are required to keep context
            this._mouseMoveDelegate = function (event) {
                return that._mouseMove(event);
            };
            this._mouseUpDelegate = function (event) {
                return that._mouseUp(event);
            };
            $(document)
                .bind("mousemove." + this.widgetName, this._mouseMoveDelegate)
                .bind("mouseup." + this.widgetName, this._mouseUpDelegate);
            event.preventDefault();
            mouseHandled = true;
            return true;
        }
    });
Now at the function calling event use mouseButton : 3 for right click and 1 for left click