It's probably difficult for the Gran to see that your daughter (obviously as you live with them) sees your parents more frequently. Perhaps jealousy comes in to play (infantile but sadly, some people work like that.)
Stop bending to fit her schedule. Make arrangements and stick to them. If needs be - a day a fortnight or whatever - I don't know what would work for you.
I know it's difficult if she wouldn't use the same routine but that's family.
Your daughter's only two though (right?) so she's still your baby and I can see why you'd not be happy to leave her overnight.
However, never say never. Say you still think she's too young to sleep over but let her go for a day out with them - arrange to do something with friends or maybe something constructive like some work or DIY and pick her up at an arranged time (e.g. 5pm so you can get do her tea and bedtime routine).
We grew up with both sets of Grandparents 3 hours away so I never had sleepovers growing up but my kids have as my parents and mother in law are local to us and it's perfect for babysitting.
Do you work? My mother in law and mum share the childcare while I work and this was a good way to build that trust as I needed it to happen!
I know it's not so simple when you're not with the father and have no contact with him. I do have a stepdaughter but the relationship between her and her dad and her mum and him and me is fine and she's slept at all 3 sets of grandparents.
Don't let her bully you or guilt trip you with her tears. It's pathetic (on her part).
My niece has no contact with her dad (loooong story) but has a good relationship with his mum - she sees her most weekends and goes on holiday with her. She's 10 and it was a long road with her dad but the contact with her nan has been important to her.
At the end of the day, it's up to you. The whole lost baby reborn thing is odd to me but some people think like. Rather spooky and unfair but harmless.