Following is just my prediction that this might be the case depending on all the clues that we got since dadi came.
I feel that due to some unavoidable circumstance Khushi's mom worked as a servant at Mallik's. Arnav's dad lusted for K's mom (just like Shyam was for Khushi), but she was in no way romantically involved with him. It might have gone out of hand when K's mom refused to acknowledge his so called love. In his madness, A's dad might have decided to give divorce to A's mom. A's mom knew about his lust from a long time and was tolerating thinking that no one knows and also for the sake of kids, but dadi also knew about that and she felt that it was K's mom's fault, as she was the servant.
On the fateful night A's dad might have spoken his feelings for K's mom out loud to his wife, and made his intensions of leaving her for K's mom clear. After that he would have left the house. A's mom in her extreme grief might have commited suicide.
Now we do not know how A's dad dies, so I will leave it at that. After knowing that A's dad was madly after his wife, K's parents tried to leave the town and in the process met with an accident and died. K was saved from the accident and was adopted by her aunt.
Dad sees the resemblence of K with her mother, that's why she does not like her, but I am so wishing for the Shyam angle to be true.