Everything that he is doing to Mukti is a type of healing process for her, whether he knows it or not. If he had just left Mukti alone after her refusal, then all the pain, all the hurt would still be stuck inside her and she would never have been able to come out of it fully. But thanks to Prem, all of that bitterness is coming out of her, in the form of their little fights and arguments. Now she looks at Prem and instead of crying over him and cursing him, she remembers that he's just an idiot.
Pretty soon, all of the pain (that she got from Prem, not Sharad) will have dissolved and then they will be able to move on to the next stage.
So Prem is not a COMPLETE duffer after all...he knows that to get Mukti to forgive him FULLY, he needs to get that bitterness towards him out of her system. These little irritations are not difficult to shift, bu the real pain is far more so.
He's healing her heart.
They are doing what every couple inevitably does, but they are doing it before they become a couple. They are getting rid of their egos and fighting about everything under the sun. Most couples have these ego and power play fights AFTER marriage and/or relationships, but these two are getting it out of their systems now. By the time they do get together, there will be nothing left to fight about.