NowI have an image in my head from an ad where a woman have her fridge filled to the brim with cabbage
Seriously I don't think this will work very well. The point is to just eat cabbage for some time right? If I tried to eat just cabbage for lets say 3 days. I would be really sick of cabbage for sure and I also believe I would overeat on all the 'good' stuff I missed out of as soon as I was back to normal eating, which probably would have lead to me gaining all the weight back (and some)
Maybe you should try to talk to your niece about healthy life change instead. And maybe you can do this together and also exercies together. Diet and exercise are much easier and more fun to do when you have someone to do it with.