Rights of a Parent whos Parental Rights have been Terminated

Hi,My husband and I are in the RFA (Resource Family Approval) process hoping to gain placement of our nieces' two boys. Without going too much into it, our niece lost custody of her almost-two-year-old son when he was 3 months old and he's been with a Resource Parent since then (about a year and a half). Needless to say, her parental rights have been terminated due to the failure to complete the reunification requirements and the inability to stay clean. The father is unknown.She gave birth to her second son who was both addicted and a preemie. He was removed from her custody immediately after his birth. The father is known this time, however, he has already made it known that he has no interest whatsoever in the child nor wants custody of him. Due to having two children being removed from her custody, her inability to stay clean or attend rehab, etc. she also lost her parental rights to the second child.Our niece's mother, my husband's sister-in-law has been attempting to gain custody for two years, however, due to her own personal housing and income issues, as well as the inability of the CWS/RFA to do anything competently, including losing her application twice, she has still not been approved despite being the preferred placement family member. My husband and I are almost complete with the process and should be approved soon, however, we've been in a tug-of-war between who will be gaining placement of both boys. We have the room and resources to house both boys. The maternal-grandmother does not and the court is already considering separating the boys. At one time, the maternal-grandmother told the caseworker she was unable to continue with the process and wanted the kids to go with us as at least they'll still be in the family, however, she has since changed her mind and is still continuing. Plus, now the biological mother, our niece, her daughter, now has a lawyer who's petitioning that the boys go with the maternal-grandmother (because she'll hand them back to their biological mother).My question is: If the biological mothers parental rights have already been severed due to negligence and abuse, why does she still have a voice in the placement of her children? How much of a voice does she have in the children's welfare? If the children are placed with us, does she have a right to take us to court and attempt to fight for custody with her mother?We're concerned with the prospect of a huge family fight involving lengthy court proceedings and lawyers. All we wanted to do was bring both boys home with their family community. Keep them safe. Grant them stability. Thanks in advance.