After she leaves for school, take the rabbit to a small animal boarding kennel (ask your vet). When the kid comes home from school, tell her this;
"You know how I have to nag you about cleaning Fluffy's cage? Well, after you left for school, he started coughing/sneezing/puking and I had to take him to the vet right away. They said this happens when the cage doesn't get cleaned often enough. You know that he's your responsibility and I haven't had time to take care of him. They're going to keep him until he gets better and in the meantime you need to clean everything or he'll get sick again." And no, she can't go visit. The sooner the cage is clean, the sooner he comes home, which could be tomorrow if she gets everything ready for him right away.
Watch for the reaction. If the kid cares, she'll panic. See how fast she cleans the cage. Now is the point where you have to decide how much she loves that rabbit and whether it's coming home or 'dies' at the vet (to be taken to a no-kill shelter). If she puts the chore off even for one day, ask her if she really wants Fluffy back or if it's too much responsibility for her. Force her to make this decision and give her the option to re-home him if she can't take care of it.