I am hesitantly going to respond. I totally understand your anger and your rant. But sometimes when I rant, I have a hard time letting go of the anger. You may be different. So this is what works for me. It may not work for anybody but me, but I try to take a different angle.

What she did was wrong and needs to be confronted. I try not to let my imagination run too wild, so I always give the benefit of the doubt and very charitably make the assumption: "oh, she does not know" or "oh, she does not know how."

Then I would approach it as: I saw the car seat I gave you was not in your car. I would hate for your child to be injured or for you to get a ticket. Would you like me to show you how to fasten it in your car?

That keeps me from being accusatory and attacking and it keeps my anger down. Then if she does not listen, at least I warned her.

In my state, there is a site on line where you can annonimously report people not using child safety seats. After I had warned her, I would consider that for the safety of the child.