There are scooters that can be taken apart in pieces and fit in a trunk. There are not as large as the all-in-one-piece models, but I think they are just as comfortable. Talk to the rental company and tell them you want one that can be taken apart, and they will see you get what you need.
They are typically very easy to assemble and disassemble into 4 or 5 pieces. The heaviest will be either the battery or the rear wheels (with the motor) which will be about 30-35 pounds.
If your mother is OK walking around the resort, you can leave the scooter in your trunk and just take the battery in for charging every night. This will save taking it out and putting it back in one extra time per day, but someone will need to be able to carry a 30-35 pound battery to the room. (Or bring a foldable luggage cart or such with you to tote it.)