When he came to know of Adi doing the accident, he should have first comforted the scared, crying boy, and explained first hand of what Mrs. Iyer's state had become and what could have happened. He should have also told him the punishment he could have got for this crime, and what life in a remand home in India is like. That his whole future would have got spoilt for ever.
When Adi would have accepted he was wrong and realised his crime, he should have told Adi that he would definitely save both him and his Mom but he would have to take up a punishment on the side + should have secretly manipulated Shagun to let Adi spend time with Raman (pushing Adi to apologise at this point would have only caused him to rebel as he hates the Iyers)
This could have brought Adi closer to Raman as Raman saved him from going to jail, and he would feel inclined to spend more time with Raman on Bala's prodding too. After some time, as Raman and Adi get closer, and Adi shows true signs of remorse, Raman or Bala could have nudged him into apologising to the Iyers. This apology would have then made more sense as it would have been from a boy who has got his punishment, realised how severe his crime was and how lucky he was that Iyers didn't make a case against him.