Also, Ishqi perhaps fails to recognise that her word alone (she says she'll ensure the kid is supported because she was an orphan herself) is not really a strong enough motivation for Rhea, and Dadi's offered incentive has far greater value.
That being said, Rhea's otherwise always been decent to Ishqi (apart from the kidnapping part), so Ishqi doesn't really think of Rhea as the double crossing/scheming type.
Moreover I think Ahaan Ishqi both think Rhea as the dumb one. The dialogues in Resort like Is bechari ko to kuch samajh hi nahi aa raha hai, itni akal to Rhea me bhi hai, made Ishqi trust with the proofs.