There are two separate laws that apply. There is a very liberal statute allowing grandparent visitation. See my website for explanation. There is a much more difficult to establish right to pursue custody. My website also explains that. You may also call my office to discuss your options.
I am exclusively a family law attorney, practicing primarily in the metro Atlanta, Georgia trial courts. However, I handle appeals from anywhere in Georgia.
This is very fact specific so you should co silt with a family law attorney on this issue. If both parents are fit parents, then it is harder for grandparents to get rights. If the parents are unfit, there are cases when grandparents have won custody. It will depend on the specifics of your situation.