Can me or my mom get into any trouble if I was to move in with her without my dads permission?

Your mother can, yes.
Compromise is always best - talk to your dad about the need for a grown girl to spend time with her mother, and work out some visits, longer ones if you have some already. Don't get into how much you like or don't like either parent.

Assuming that dad has court ordered custody, you cannot move in with mom without court approval. Mom would, therefore, be violating a court order.

Mom would have to go to court for a modification of the custody order for you to move in with her. If you are "almost 18" then its likely you might turn 18 before it comes up in court.

Your other alternative is for dad to agree with the move. I would make sure it puts it in writing. Even though a private agreement doesn't modify the court order, it may keep mom from getting in trouble.