Lets be practical yaar, this is how the rich spoilt brats are, he loves his brothers that is a different matter, but he has seen people bowing down to him for money, it is not just Anika, it's with everyone excluding his family, whenever someone tells him that it is wrong he just throws away the currency notes, and people forget everything & start collecting the money, I think he gets some sadistic pleasure seeing people bent down in front of him, even in yesterday's episode he just scolded the lawyer when he was telling how the plan would be executed.
He knows that he is from the most powerful family in India and can do whatever he wants, hence when he saw Anika challenging him, he couldn't bear it.
Then when he saw Om lifeless in the pool he couldn't tolerate it, for him his brothers are his life, at least Om has some concerns for his mother, but Shivaaye seems to care only for Rudra and Om, he chides away his mother when he is with his brothers, he feels that this all has been caused by Anika and hence wants to destroy her. I agree he should have done some investigation before blaming Anika, but excluding that all his actions are perfectly justified.