I love your OC Rosemary and I choose to believe that Edith heard about what was going on and sent Rosemary what she needed to get out of that household
Well, not Edith but Lucille
I was thinking they had no idea she even existed until she turned up at their door prepared to argue her way into the household- the siblings don't seem the type to keep in touch with distant relatives, and if Beatrice was the oldest of Many (bios), there are a lot of those. Sufficiently observant abused child + unlimited access to rat poison and also soup + society that doesn't really think little upper-class girls capable of much at all due to the combination of Child, Rich Family, and Female = relatively easy murder. Lucille got away with poisoning her father at age 11, after all (bios).
Honestly, I feel like Edith would be more likely to get curious about the other Chetwynde siblings (Beatrice's canon maiden name, bios) and their children, if any of the OT3 would. As an outsider, she doesn't have the same reasons to write them all off that Thomas and Lucille do.
Maybe she began wondering, did some digging in Burke's Peerage, paid a call, noticed that Beatrice's sister and her husband seemed appalling and there was no sign of the daughter they were supposed to have but also some brief, dismissive mention proved the girl was still alive...and added things up in her head.
I still may stick to "they never knew she existed," but it's an interesting thought to play with!