As stated above, the fake eggs are only needed if there is danger of her own eggs actually hatching. Go ahead and leave her eggs with her.
There are a LOT of things you can do to disrupt the hormonal cycle. I started researching this as an adult because when I was a kid I had a cockatiel lay herself to death (dozens and dozens of eggs a year) and I had no idea how to stop it. I have written an article on hormone control which I will link here for you
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Cockatiels:Battle, Sniper, Jackie, Honi
Blue Headed Pionus: Mel
Green Cheeked Conures: Flick, Cache, Titan
Indian Ringeck Parakeets: Blue, Kamehameha, Ka'iulani, Kahili, Shadow, Ali'i, Noni, Pono, Smokey, Hapu'u