morning Indigo, maybe it's not too late, if your mom is only concerned about the odor here is a list of things that might just make everyone happy:
#1 size of cage, make sure it can hold 6 rats
#2 what bedding are you using? pine or cedar really stink you may also look at how often you change them as well as using a litter box and having less mess
#3 air flow, I'm nuts about it, being an asthmatic. create an inlet and exhaust to your room going out the window, so have a fan at one end,away from the cage, and a reverse fan sucking air out in the window, this will help, as when my son was living at home, this is what he did for his rats in his bedroom.
Have your mom come online and ask us as well, we can help, at least give it a trial.
Caring for rats is not an easy undertaking, maybe you need help with the husbandry ( care of animals) all together