Look at the balls used in the cage?how hard or soft will depend on what it does to the bat. She should also be rotating the bat in her hand after each swing to break it in properly. You have read about the bat rolling and mallets etc used to modify the bat properties?well using them in a cage does that also depending on the hardness of the balls.
If you leave her bat in the car and the temperature was let?s say 20 degrees and the temperature in the cage is probably 60 to 65 degrees, you will most likely damage the bat.
Most bat warranties are 65 degrees not less and it takes a little time for the bat properties to normalize or come to room temperature, so try to keep the bat in the house and buy or make a sleeve to keep it warm. Transport the bat in the car not in the trunk.
In my opinion a bat the has the same weight and length is OK to use in a cage as we are not hitting for performance or distance, however we are working on technique and mechanics. Having a good grip on an old bat gets them the feel in their hands and good grips are 8 to 10 dollars and try to use the same grips. If you have deep pockets it is a mute point.
Howard