If I were her mentor, I would supervise her while she is grooming and tacking up the horse. If she doesn't pick his hooves out for example, just say nicely "Don't you remember that we have to pick his feet out before and after we ride? We don't want him to get sore feet do we?". If she is stubborn, then just say "No, we are not allowed to ride our horses unless we look after them properly. It's part of the responsibilty of being a horseperson and it is very important."
She's only eight. I know that she's old enogh to do things for herself, but she probably doesn't understand the consequences of her laziness.
And after a ride, if she goes to the roundpen again, just say "I think he's had enough work for today. Why don't we just untack him and let him relax" And again, if she's stubborn, you just have to be more stern. As her mentor, I would personally think that it was partly your responsibility to make sure she is treating her horse properly. Isn't that the whole point of you being there?
Whoever said money can't buy happiness didn't know where to buy a horse.