Having read your additional information Poseidun I will admit to changing my opinion. 
If they are as unreliable, controlling and devious as you say, if you've tried to talk this over and gotten nowhere, then your little ones are best kept away from them.
At their age, they shouldn't even be aware of what the grandparents are doing but as they are, and cry as a result of those actions, you'd be better protecting them from such possibilities in future.
Don't talk about it in front of them and explain in an age-appropriate way that they won't be seeing these people again.
The old people are never going to be the grandparents you want, whatever you do.
My father tried to keep up contact between me and my grandmother because he felt it was the right thing to do but those visits, and her actions, were awful and I still remember them 7 decades later 
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