In Texas carrying a concealed handgun in a vehicle is allowed. It is not allowed to display it when not in immanent mortal danger, to yourself or someone else.
Pulling the gun out in the event of an unlicensed, uninsured person hitting your car (civil offense) is a criminal offense, with you, not the other driver going to jail.
A gun is a tool, but not an all-purpose one.

OP, that sure was nice of you. I would have called the police and gotten a report on record regardless of her situation, just to make it more difficult for her to come back and sue me later.

If she didn't want to get in trouble for driving without insurance or a driver's license, then she shouldn't have been driving without insurance or a driver's license.

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617 swapped Toyota Pickup, 22-24 MPG, 50k miles on swap