The DMV says that you can indeed get insurance coverage in Maine even though the car is registered to your mother on the opposite end of the country. Luckily, the insurance coverage does not terminate whenever you leave the state that the car in question is registered in. If that were the case, people would be in big trouble if they were in a car accident while vacationing in another state, but I digress. Even though you are still able to be covered by the insurance company in the case of an accident or just in general, it is important to register the car in the state you reside in as soon as possible if you have moved to Maine or if the car is a gift from your mother in Florida.
Obviously, I do not know much about the situation at hand. I hope that I have been able to be of help to you today and that I have given you the answers or guidance that you requested. If you have any other questions or concerns, please feel free to contact me or your local DMV. You can also go to the official DMV website to obtain any other information you may need. I hope you have a wonderful day!