Malini blackmailed/manipulated Adi completely here. She is blind and unable to see the injustice served to Bansal family and innocent kids. She tried everything possible to stop Adi from revealing the truth to Kavya..
Its not like Adi's trust in their love is weak. If it was true, then he would have been silent. He knows he is not involved and he trusts Kavya that she will understand and will not go against him. That's why he is attempting to reveal the truth to her repeatedly, but being interrupted by Malini..
He knows he may loose Kavya if he hides (thats his guilt), because she will find the truth as she is working on the case and she will find out he hid from her. But, being silent he may save his mother. Understand that, besides/before Kavya, Malini is the only other person who he believed to be good/not like his father/brother or trusted the most..