Admittedly, in the beginning Radha was a meek and naive character. But she was easily impressionable and manipulated by Rashi, Umaang and Tripti to their whims and instigation about Gopi. But why was she so readily to believe that Gopi wanted to snatch her happiness? Well consider this. She grew up in the shadow of an elder sister who was 'lost.' Her mother in her grief was in no position to care for her and hence she may have grown up without much concern and care. Fast forward to the family reuniting with Gopi many years later and Radha sees that although raised as an orphan Gopi was enjoying a happy life. Jealousy will raise its head. I feel that without interference by Rashi et all Radha may have harboured I'll feeling towards Gopi.
I beg to differ. Radha was never, ever jealous of Gopi. I say this because she created misunderstandings betwen Raji only after Rashi put a letter in Ahem's box that led to a tiff between Gohem. She said, "You tried to create a rift between my sister and jija, now I'll do that to you and your hubby."