Without knowing you or your parent, nor much about your situation, there is one reasonable deduction I can make: your mom does not have confidence with you in traffic. My suggestion is to address this by finding some local group rides, and participate in at least several of them. You will learn the necessary skills and will be able to reassure her.

If your mom balks at that step, that's where I'd suggest insisting. See if you can find a group that starts somewhere near the trails that you can access so that you don't need her to drive you there (unless you can drive and have access to a car, then just go).

After that, one strategy is to ease into it with short rides to the convenience store, around a block or two in the neighborhood, and gradually increasing the time that you're out. It's easier to build up than to have a big fight about the end goal all at once.