Concerning the thing with your car, pointing out that not driving it for a while will help save money that you don't have at the moment should help to make your mother cooperative here. Of course, if she is to drive you around (even if it is only on few and far between occasions), that means extra work for your mother, so I think you should offer something in exchange to make up for the time she'll have to put into this. Try to think of any household chores you could do for her. If there is younger siblings and/or pets in your family, offering to help to take care of those may also make it sound worthwhile to your mother. Try to find something you think she would apprecciate some additional help with and that adds up to about an equal or slightly greater amount of time saved to her than she'll need to drive you around.
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Yes, I am serious about that avatar...