Dear Aggelos,
If you want to encapsulate Mootools off within YUI so that there is no conflicts then you can use a YUI custom module. A while back I was working on the jQuery issue with Andrew Nicols and came up with the following change to the MyMobile theme to encapsulate jQuery, jQueryMobile and it's custom script - https://github.com/gjb2048/moodle/commit/60e815e8a388cab74218209db1cdc7d382c45b9b. With it you can then either have a custom script or put the custom code within the 'YUI().use'.
The code snippet that it references is http://jsfiddle.net/andrewnicols/WaFDA/.
I'm sure you could adapt it for Mootools.
Cheers,
Gareth