Sorry to hear about her troubles
It doesn’t sound like a weather problem to me. Sneezing is not normal and could indicate an Upper Respiratory Infection (URI), which can be fatal. While water consumption can increase in warmer weather, it is often also caused by dental issues because many rabbits with teeth issues would drink more to soothe the discomfort in their mouths. Since you mentioned that the bunny’s incisors are not even, that could indicate a teeth problem and the molars would also need to be checked (which can only be done at a vet’s).
If the bunny is shaking its ears excessively, this could indicate a mite problem or an ear infection, which would again, also need to be assessed by a rabbit savvy vet.
One way is to call up a rabbit savvy vet in the area and have them explain to her parents the need for a vet in this particular scenario. Lots of parents do not listen to their children because they think they know better, but a professional, rabbit savvy vet might be more convincing.