Sadly you have not taught your kids how to properly care for pets and you have let them have tantrums without consequences. When a family gets a pet, its the PARENTS responsibility to TEACH the kids how to take care of a pet. You cannot expect a child to be 100% in charge of the pet to feed, clean, etc.
And by letting the poor rabbit live in filth, you are risking sickness to the pet. So start by putting up a chart of when the cage is to be cleaned, rabbit fed, etc. and your child MUST check off when its done. At first show her HOW to properly clean the cage and supervise her doing this until she knows exactly what she is to do.
My mom's rule regarding pets in our house was that if we didn't take care of them, they would be gone. We learned very quickly (with no tantrums) how to care for a pet so it would stay with us.