I've had the problem with green horses. Out on trail rides and they get sweaty and want to roll. In my case usually in deep snow or relly sandy sections of the trail.
Once I find out that a particular horse has those tendencies, I had to be very proactive about stopping it. I find that my horses always start showing signals of wanting to roll. Head down, pawing etc. I have to immediately put them to work at something. Move off my leg, Dance around a sagebrush, Just ask them to do something so the have to focus on you.
Educate your daughters to the signs that the horse is looking for a good spot to roll. Tell her when she see's those signs, she needs to take control and not let the horse have an idle mind. Nip it in the bud before the horse ever gets his knees on the ground..
I had to TEMPT my horses. I know they like powder snow or really sandy spots on the trail. When I was in spots where I knew they were thinking about it, I would give them a little slack and watch for them to start looking to roll. As soon as I'd catch them, I'd correct them and put them to work. Only took them making the mistake a few times and they learned not to do that under saddle.