When you have jQuery specific code that is using $, the simplest way is to wrap the code with the following:
// Disable the $ global alias completely
jQuery.noConflict();
// For jQuery scripts
(function($){
// set a local $ variable only available in this block as an alias to jQuery
... here is your jQuery specific code ...
})(jQuery);
// For Mootols scripts
(function($){
// set a local $ variable only available in this block as an alias
// to Mootools document.id
... here is your Mootools specific code ...
})(document.id);
See the second example on noConflict documentation.