Oh my. I moved out when I was 19 also...hardest and best thing I've ever done for myself and my mother(although she vehemently disagreed at the time). My situation was not as extreme as yours and I didn't have any pets to consider. The others have given good advice. I knew with my mother that once her mind was set arguing or reasoning is useless...so my temporary move to my Grandmother's became permanent when I told her (after being there for a month) that I wasn't coming back. It was hard and it took a good year for us to get our relationship back. This may not be the best advice in the world and by all means don't listen to me...but when you move just take kitty with you..when she isn't looking or move kitty before you actually move. Basically if you know that your kitty's well being will not be taken care of, do whatever you have to to ensure she will be with you when you move.
(hugs) and Good Luck.