That's certainly a tougher one. Some people never learn to look around. The term they used at the ASI training for this was SIPDE. It's an acronym that stands for (S)can the area, (I)dentify obstacles and pathways, (P)redict what will happen for each path you can follow, (D)ecide on a course of action and (E)xecute it.
We do this naturally every day when driving our cars, riding a bike, taking a walk, and riding our ATV's. The difference is the matter of speed. In our cars, on the road, with everyone going the same way and speed, SIPDE isn't as important as ATVing. While we may bike or walk down trails, the speed is so much slower than ATVing that SIPDE becomes a non-issue, but on an ATV, off road, on trails or on the track, things can happen fast and our observation skills become so much MORE important.
With my kids I began by teaching them that concept. I drilled into their heads that it is so much MORE important to be aware of their surroundings on an ATV because the danger was so much greater than their other activities.
You might try some visual demonstrations. After talking with her about the importance of extra vigilance necessary for ATV riding you can have her try lifting the ATV. She won’t be able to as even the small ones are over 200lbs. Let her try for a while, though, from both the front and the back. This should illustrate to her just how much heavier this piece of equipment is than her bicycle (which she probably CAN lift). If you have access to pumpkins or watermelons or some other squashable item that you don’t mind sacrificing, run them over with the machine. While a human head is a little more resilient than a gourd, it can still illustrate the destructive potential of the machine.
Did she scratch or dent your girlfriend’s truck? If so, make her PAY for it. Perhaps not all of it, but have her do some things for you or your girlfriend (clean her truck, etc) that are real work so she understands that her actions have consequences. Have her do some things for her brother too (like clean his room). This may seem a little harsh, but it prepares her for “real” life as an adult.
Set up an obstacle course for her and you to ride. Make sure there are turns and different courses she can take. Then when she rides, watch her head, see where she’s looking. If she’s not looking where she’s going, if she goes too fast around an obstacle she can’t SEE past (like a car or building), if she does ANY thing that seems unsafe to you, stop her IMMEDIATELY and explain to her the possible consequences. You may have to limit the ATV’s speed to a crawl to do this, but it’s extremely important for her to learn this skill. I won’t let a child under my supervision ride that doesn’t show proper attention (and I have had to pull some off the machine on occasion).