First of all, my bro just graduated with a Math degree and unless you plan on being an actuary, which requires a bunch of expensive tests, there isn't a lot of career options with just a Math degree. But you can probably say the same thing about a psychology degree too, so my advice is that if you are paying for it then go with what you enjoy.
I am 25, have a degree, own a house and have a respectable job. I couldn't have gotten here without my parents help (regardless of how annoying they were). I am not going to pretend I know exactly what you are going through, but I will give you my advice.
Fulltime jobs that do not require a degree do not pay a lot. With an apartment, a car, and bills you are really going to be strapped for cash every single day. You might need to find a job that you can put extra hours into every week. You are probably going to need to work nights and/or weekends.
The biggest issue I see with this is that you plan on going back to school. School is VERY expensive and you probably won't make enough to afford it and all the things you want with your freedom. Taking a semester off from school might void your scholarship as well so make sure you look into that.
In my life, lying/bending the truth has ALWAYS ended badly. I have seen them irrevocably ruin friendships and relationships. I think you should tell your father the truth. Better now than later.
If you truly have no love for your father I still think it would be foolish to break your relationship simply because of the resources he gives you for school. Transportation, money, and shelter are worth a lot for a college student.
Assuming you are trying to get a 4 year degree, I think you should stick it out for that last year before you break from your parents. It will be VERY hard to finish school if you don't have that financial backing and have plenty of new bills.