It does not matter if she has the right to do it she can do it anyway. If the father does not claim the child chances are he will not be interested in custody anyway. She can also report you as unfit any time she wants to which does not mean that you are. As long as you know that and you are able to take care of your child by loving and providing the things he needs you should not be worried about what they talk about. If he does try for custody he can't do it without you since you would have to be notified. Hopefully you and your sister can work this out. But if she is doing anything to confuss your child I might consider if he should be going over there or not. But don't use your child because you and your sister are on the outs.
I live in New York State. My son and I lived with my sister and her family for almost 2 years!! Now that my sister and I are no longer on amicable terms and she won't allow me to be in her home. I don't feel I should allow my son to go where I am not wanted. So now she wants to contact my sons father..who i know does not want anything to do with him..to try and talk him into asking for custody...joint custody anyway..does she have a right to this? She can't prove me to be an unfit mother...so can she even do this? he lives in a different state and pays an extremely minimal amount of child support...He refused to believe that my little boy was his son...then at the support case he wouldn't hardly admit that my son was his even when the paternity test came back 99.99% and knowing this he refused to take a picture of him. and he also told the judge that he guessed that my son was his...but then the judge made him say that he admit to it. so all that aside does my sister have a right to do this?