Whenever you DO tell her...
prepare yourself ahead of time to be as gentle as possible, and DO NOT get into any arguments, even if you think she is provoking you, and even if you feel your blood pressure going up as she says whatever she may say while she is hurt, guilty, angry, or whatever. Just remember that it will be over soon, you will be gone, and you will be happy to have left on the most positive note that you can make happen. Please do not burn any bridges behind you! You may be absolutely sure you want to live with your dad, AS OF RIGHT NOW. But in a few weeks or a few months, you may decide you wish you could live with mom again. If you can control the natural tendency to argue or tell her what she has done wrong, then that option will probably still be open, even though you probably think you really never will want it - at least for right now - anyway. If there was ever a time that being mature beyond your years will benefit you in the long-term, this is it, lol!
It is a good rule of life to try to keep as many options open, as long as possible, until you are ABSOLUTELY certain that a particular option is not ever going to be viable for you. It is also a good rule to realize that the younger you are, the more important to keep more options open. That is because you are still growing and maturing, and there is no way to know today what your passions and goals will become over the next few years.
Hope it works out well for you to live with dad!