Hi, I really empathise - I had a baby like this too and it can feel like such relentless, hard work with no break at all sometimes.
I think you are thinking along the right lines when you say you might leave her with your parents for a bit. If you do this regularly and gradually increase the length of time, perhaps she'll eventually be calmer with them.
But before this, when you are with your parents, could you try and all play together with your daughter? Essentially trying to show her that you are comfortable with her gran and grandad, so she can be too.
I used to always wonder if the baby could pick up on my anxiety/worry. It was hard for me to switch it off when he'd spend the entire time crying whenever we went to someone's house or had visitors ourselves.
When you go to your parents' house, what do you do? Do you all sit down for a chat? If so, would it maybe be easier for the baby (at least to begin with) if you walked around with her (with gran or grandad), showing her things, for example?