aarthi was both right and wrong
As family you have duty not to gossip about family matters outside house and to mainatin secrecy. Hence arthi told buaji not to call and tell everyone about akash and radha.
Yes all those in house that day when arthi told truth will go and tell other but arthi was forced to do it. Do you thnk anyone in scindia family that day would listen if arthi says "Please come inside house all of you, i have to make a disclosure". Arthi tried her best to tell yash many times when he was alone but he was not ready to listen hence arthi had to tell matter in front of outsiders. But here buaji can keep quiet still calling everyone and instigating against her brother.
In a way buaji was correct as she is concerned about gathri's status in house after radha too living in same house. No one is bothered in house to care for gayathri so buaji had to call outsider to tell what is in her mind about this matter. Gossiping in family happens when family members refuse to listen to others views then they call outsiders and tell as they have no one to listen inside house.
So we cannot blame both woman both are right in their own ways.