Does the language school know that you are contracted for full-time employment?
My understanding is that to work part-time in the UAE, you either need to be under the sponsorship of your father/husband. Or if you are on employment visa, then you need an NOC from your sponsor.
<em>edited by em2san on 30/01/2012</em>
Well technically you are breaking the law, as unless your sponsors give you permission to do outside work it's not allowed. Most employment contracts actually state that employees are not allowed to work else where as well.