There's always a danger when you use nonstick cookware around birds. The teflon coating can put off a gas when it is scorched or burned (it's actually dangerous to people as well, but we are much more tolerant than birds are), so if you do use non stick, you have to be sure to never use it on a temperature above medium high to ensure that it won't burn, and never ever leave it unattended. Keep the birds well away from the kitchen. You can cover them as well, for added protection. Always run the kitchen vents when cooking. If you have an outdoor patio on which you can use the George Foreman grill, I would to that, too.
It' is always safer to use cookware that is not nonstick, like stainless steel, but it is also very expensive to purchase GOOD stainless cookware. You will probably have more luck convincing your mother to be very stringent about not cooking on high with the nonstick than getting her to buy all new cookware.
Always watch your birds for any unusual signs or unusual behaviors. Birds hide their illnesses, so they won't look like an easy meal to a predator, and so their flock won't abandon them. Seems silly to say, since we'd never dream of booting our birds out, but it's Parrot Psychology 101. If they are not perching and hanging out on the bottom of their cages, have ruffled feathers, have labored(heavy) breathing, feel cold, seem weak, or have any sort of eye or nasal discharge, something's not right and they need to be seen by a vet right away. If you're careful with the nonstick, you shouldn't have any problems. I still have a nonstick pan or two that I use, and my birds are all as healthy as can be, but I am extremely careful in how I use my cookware.