Elsa was sad, angry, lost and confused, but granny foresaw that that would happen. I believe that is one reason she gave Elsa the apology letters to deliver. That gave Elsa something to do that would at the same time remind Elsa of granny, take her mind off her grieving, and help her understand reality. Brilliant!
Why do we have such complicated feelings when we lose someone? We miss the person, even if we had mixed feelings about him/her. We might question God or a higher power - or the person himself. If we know the person was in pain, we might feel a sense of relief. Because we are human, we experience a mix of emotions we often cannot understand, maybe more when we lose someone than at any other time.