Open Adoption Legal Question

I am a distant relative attempting to adopt the two children of my cousin. My cousin and his wife are seperated. They both are drug users and parental rights have been terminated. The children are now in the state system awaiting adoption. It is common knowlegde within the family that the birth grandparents also use drugs but I have no way of proving it officially. It is one of those dark family secrets. In our home study my husband & I stated that we were not opposed to contact with the birthparents with the stipulation that they would have to be reformed - have gone through rehabilitation and proven stable & clean before we would allow a contact as we do not condone drugs or want to subject these children to the even more complicated emotional trauma of interacting with drug users. We did not bring up the issue of the birth grandparent's drug use but are very uneasy about the children being in contact with them. Since I am a blood relative I do not have the option of a closed adoption and we do want the children to benefit by continuing their relationships with the more stable people in our family. My question is this: If we are able to adopt these two children in an open adoption situation what legal rights - if any- will the birthparents and the birth grandparents have in reguard to contact with these children?