Grandparents don't have any special rights. You do, and need to file for custody. The Court decides on custody based on the rule of thumb of "best interest of the child
." This includes, but is not limited to, general stability of the parent, financial stability, indoctrination of the child in the current school and environment, household condition and living condition of the child, other persons living in the house, etc.
The courts generally do not like to split the custody 50/50 since this is hard on the child – imagine having to move every half a year.
One parent usually becomes the main caretaker (in many states this is called the managing custodian) and the other parent becomes the "weekend" parent (often called the posessory custodian) which is every Thursday, every other weekend, and alternating holidays. The minute points of the custody can either be decided by the parties or the Court, if the parties cannot come to an agreement.
Even if a parent does not get managing custody, they are almost guaranteed the posessory custody unless they have a drug problem, alcohol dependency, or an unsafe home environment. Abuse and or neglect of the child or previous children are an almost automatic bar for even posessory custody, although supervised visitation
may be granted by the Court.
The posessory parent pays child support
to the managing parent, unless the managing parent declines it. All states have a preset salary percentage calculation for child support, but this can be altered if both parties agree to a lesser or higher amount or do not put child support in the orders all-together - the Court will not care.
Best of luck in your matter. I'm here if you need any more clarification or follow up info.
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