There is no automatic citizenship of the baby unless they decide to keep Anna's citizenship. If they revoke Anna's they then revoke the baby's also. (yet another nightmare)
Personally I think that the Bahama's will wipe theirselves clean of all this. They will revoke Anna's citizenship and the baby's also - erase it off the books. The baby cannot be a citizen unless her mother stays a citizen even in death and as you know Anna lied to get her citizenship.