Sorry you are having this experience with your parents. Mine were not the best either and more or less kicked me out.
I understand why it is scary that they may cut you off, but realistically, they are not helping you, they are taking advantage of you, especially your mom.
With the money your mom is taking from you, you can certainly pay your own way with a few room mates. If you can really get by on a bike (or cheap motorcycle in the summer) just forget about the car and be glad you don't have to pay insurance any more.
As for how to justify moving out, try and term it so that you want to show your parents you can be responsible and manage on your own. Point out you are not going to stay home forever, so why not move out now? Tell them you would appreciate any help they can get, but that you are ready to try and handle it yourself.
How you mom reacts will tell you a lot about why she is taking your money. If she gives you a bunch of BS that has nothing to do with being responsible, then you know she just wants your money for her. If she applauds it, good for you.
Once you move out, do not give her any more of your money. She could handle herself before you started getting financial aid and she can again after you move out. Right now, you are just the easiest target for money. Once you are gone, she'll switch to someone else after a while - not to mention nobody in their right mind would believe that a college students with student loans should be propping up their mother financially.
Just so you don't have to do everything at one, start by setting up new free bank accounts that your federal aid can be deposited to, once you move. That way, there is no need to worry so much about the old account.
Also, try with a cheaper phone plan.
Finally, if you want to save up a bit just before moving out, see if your employer can keep your pay for a month and only pay it out once you have moved. If you have a good boss and explain it to him/her, they may be willing to do that. If you don't think your mom would call your boos, you could also just pretend they are trying to switch you to monthly pay.
Good luck - I know it can be scary, but you sound smart and level-headed and if you stick to a good plan, there is no reason it wouldn't work.