Are you absolutely certain that she is the one purposely breaking them (do you actually see her purposely doing this), or are you just finding the broken pieces of feather laying in her cage? The reason I ask is that I've seen this quite a bit with parrots brought into the Rescue I work with, especially in larger parrots, where it's their tail feathers and then just the very back ends of their wings...and 90% or more of the time it's because the cage the bird is in is too small for it, or too far too cramped with dozens of toys, perches, hanging items, etc....Usually it's strictly due to the fact that the cage they are in is far too small for them, and they are constantly damaging their feathers every time they turn around, open up their wings, etc. Usually the feathers are damaged on the cage bars to the point where they are just hanging there, and at that point the bird may pull them the entire way off, or they just fall off.
I don't know what size of cage you have your Grey in, but as I'm sure you know, an African Grey needs a very, very large cage in comparison to most parrots...I'm assuming your bird is a Congo African Grey? If you haven't ever actually seen her purposely working on chewing her feathers off (I'm not talking about daily preening, that is totally normal; they have to really work at their feathers for a long period of time to actually break them all off as you describe), and you're just finding her broken feather pieces laying in her cage, you may want to consider the size of her cage. Just an FYI...
Otherwise, if your Grey is actually working at her tail and wing feathers purposely to the point that she's breaking them off, then this is a form of plucking/feather-destructive behavior, and you need to try to figure out what is causing her to do this. I would normally tell you that the very first thing you need to do is take her to a Certified Avian Vet or Avian Specialist as soon as possible, as often this is a result of a physical illness or injury/pain that the bird is in, there are a ton of physical/health/medical issues that can cause them to pluck the feathers that are around the back of their body, such as the tail, the back wing tips, around the vent, on the legs, etc. So normally you first want to rule-out medical issues like infections in the Gastrointestinal Tract, the Urinary Tract and Kidneys, etc. The you want to rule-out any parasites, such as many different types of mites, fleas, other insects, etc. Feather mites are a common cause. If you don't have access to an Avian Vet then this becomes a problem, as there's no way to find out if it is a medical issue.
Moving on to behavioral issues that can cause this, again, there are a million causes, though with an extremely intelligent parrot like a Grey, it usually has something to do with the bird being very bored, understimulated, not getting enough attention, having nothing to do, no toys or only a few toys that they've had forever without any change, no foraging activities, not enough time out of their cage, not enough time with their person or people, etc. So you need to look at her entire environment, her daily routine, hours out of her cage every day, amount of time she gets to spend with you, what activities and toys she has to do, how many and what types, are their different types of activities for her, etc. Does she always have a "job" to do to keep her buys, etc. There is nothing more tragic than a parrot with the intelligence of a 4-5 year-old human child that has nothing to do, gets no attention, and just sits in a cage all day long by itself. I'm not saying that is what your bird's situation is, just that it's a very common situation, especially with a large parrot that you admitted doesn't get along with anyone in your family but you...
Also, what is your birds regular, daily diet? What does she normally eat throughout a single day?
) a perch for us ASAP. 
