grandparent's rights

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My 9 year old daughter paternal grandmother is getting weekly visitation and she does not want to visit with her but her cousin who lives at her house sometimes. So she has a horrible time and the grandmother is never listening and arguing with me in front of my daughter. I have a horrible lawyer who does nothing and is always losing. The child's lawyer says she can't make them stop visitation until she is like 13 and only may be able to lessen visits eventually. This cannot go on for another four yeatrs while my daughter needs me, my authority, discipline and good influences during her preteen age. Do you think this right? Is this the usual thing to do? I live in New York City.