She's using you! She should not have access to your property (like your car) when she chose to leave. When I started reading about her "reason" to borrow it, I felt it was to see boyfriend. She's smart enough to know to through certain words around to soften you up. Like going to visit her mom. She figured you couldn't say no to that.
That's pretty low.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!