You’re the one who could lose your degree and be charged with financial aid fraud. I would tell the financial aid office that you’re commuting.
Your dad won’t agree to let you live off campus because he wants the extra money. He won’t get it if you’re using it for rent. Will your parents throw you out if you don’t lie for them? The problem with moving out without their consent is that you need their cooperation to file the FAFSA, so you’re in a really difficult position.