I feel that Roshni had probably not gone far and maybe Sid called her and maybe said something to make her come back. And she would not go to DD's house, bt seriously Yash is stupid. Clearly in front of Roshni said she was not going to leave until Sid came back home. That should mean something to Yash, but he is dumb to understand any of what comes out of Roshni's mouth. Yash says he loves her bt us unable to see through her like Sid can. When Roshni left and she left the sindoor imprint on him, he was angry not at her but at those who falsely accused his wife. He was determined to get pay back. Which he did.
Even DD knows that Sid is not a bad person and would step up and take responsibility when needed, which is why according to the spoilers she will ask for his help in saving Sam when DD gets into a fix at the airport.