Does your step-brother even really want this rabbit? The fact that they keep him in a small cage which is never cleaned and that they feed him improperly, sounds like they really don’t want to bother with him and don’t really want him. Are there any good rescues in the area that might take the rabbit? Or would you know of a person who would provide a rabbit with a good home? If so, you could suggest that to your step-brother. You could also tell him that the rabbit will likely suffer GI problems as well as teeth problems since he is fed no hay, and that he could also get sick from the dirty cage, could even get fly strike. All of these problems would require vet visits, which means spending money. It doesn’t sound like they would want to do that.
If you don’t think that would persuade them to give him a better diet, a bigger cage, and a clean cage, would it be possible for you to try to find a bigger cage (secondhand, to save money) and to provide the rabbit with some hay on a regular basis? Would your step-brother bother to give the rabbit the hay that you provide, and would he possibly start cleaning the cage? If not, it does sound like you may have to get the authorities involved, even though I’m sure you don’t want to do that.