Both parents a recently deceased...Who can take custody of the minor?

In the state of TN, the mother of a 9 year old and 2 week old passed away. The father of the 9 year old passed away 2 years ago. The father if the 2 week old was incarcerated at the time of birth. Both fathers were not married to the mother. The deceased mother's father signed for emergency custody the week of her death and has both minors under his care. Even though they aren't going to be living with him. They will be living with his daughter. The father's family of the 9 year old would like custody of some sort because the home's he is assigned emergency custody to is unfit for children, meaning roach infested and unclean. The father of the infant is trying for custody on his own... Is there a time frame for the 9 year olds family on his dads side, to sign for custody and how would we do that without him being moved to foster care. They, meaning the currently assigned grandparent, are willing to allow 2 days a month visitations which is unacceptable. Please help!