I am sorry that you are going through this. Grandparent rights vary and depend upon your states statutes but regardless, the grandparents have to have ties to the children and an awful lot of advantages to change custody and your questions seems to indicate they do not.
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It is it very difficult for grandparents (or any other person) to take custody of a child away from a biological parent unless the biological parent is not a "suitable custodian", and it would depend on the circumstances. It would probably take a case of abuse or neglect by the parent with whom the child has been living.
Why would the grandparents be threatening legal action?
I would recommend consulting an attorney.
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