There are many factors that would determine how much it might cost to pursue this, including whether the mother contests your petition and how vigorously she does so. Therefore, it is difficult to put a final price tag on it.
If she did not vigorously contest it and you retained an attorney who provided you with a discount, it could potentially cost as little as a couple thousand dollars, but the price could be much higher than that if the mother does contest the matter.
State law DOES provide for a grandparent's right to petition the court for visitation rights where the parents have never been married. However, since your son's rights have never been established by court order, it would normally be best for him to file a petition to establish parental rights
and then you could intervene in that case seeking visitation. That way, the costs between you and your son would be split as well.
It is your son who would typically need to request a court order for a DNA test, since he is the one who may or may not parental rights to the child.
Here is a link which sets out the circumstances in which a court will hold a hearing on grandparent's visitation rights. If you can show that it would be in the child's best interests for visitation to be granted, then the court is likely to grant your request:
Another option is for your son to petition to establish parental rights, obtain visitation and then simply permit you to have contact with your grandson while he has visitation. That would save you the expense of having to seek grandparent's rights, but he would need to pursue the matter in court in order to gain visitation for his child.
If you cannot afford an attorney, you may wish to inquire with the local legal aid offices to see whether you qualify for low cost assistance. Or call the state bar association and see whether any family law
attorneys are willing to handle your case at a reduced fee.
I hope this helps clarify the situation for you. Please remember to rate my service once you have all the information you need. If you have any other questions, please ask me – I’ll be happy to respond. Thank you!