If it had been used in this one situation (stealing) then maybe it wouldn’t be a huge deal, I find it a little odd for sure, but only odd.
However if like you imply it was a regular tactic and they have a habit of treating family like that then I would say it’s a problem.
I can’t think of any particular name this behaviour would sit under other than what you’ve already called it, emotional abuse. I’d also call it manipulative and selfish.
There’s no way a parent should put that in a child. Sure, telling your child that what they’ve done has upset you is ok, but the sort of guilt that it is making you and your sister feel is not healthy, especially to a spongelike child of a tender age.
If I were in your shoes I would only allow my child to be with the grandparents when I was present, and not alone. Behaviour like this from your parents, if it is this extreme, shows a lack of responsibility and consideration for others feelings.
Just my opinion,
FF