She says herself that she took Aerith because she was desperately lonely. It was a good deed, done by a decent woman, but it also satisfied her own needs. Theozilla, I don't know if you have kids, but I can tell you there is no parent who wouldn't shop three wanted terrorists to an evil empire if they thought it might just possibly bring their beloved child safely home. A parent seeking the safe return of their child is not a rational being. The reason the question popped into my mind was because Elmyra clearly believed Shinra was an organisation it was possible to negotiate with. What we know of their treatment of Aerith up to this point in the game is less malign than it was in the OG.
The Remake is giving me time to ask these questions. The OG didn't. In the OG, Elmyra seemed to think that if Avalanche didn't rescue Aerith, she was done for.
But who knows, maybe Elmyra just looks into Cloud's eyes and can see that he is A Good Person.