If Alice does not sit on an edge seat, then only Derek and Eric can sit beside her. This situation also satisfies the other restriction. In this case, we first bundle Alice and her two neighbors and choose a block of three seat for them. Next, her neighbors can switch within the bundle. Finally, the other two people can freely sit. Therefore, the number of ways in this scenario is $$C_3^1\times P_2^2\times P_2^2=12$$

If Alice sits on an edge seat, then her neighbor must be either Derek or Eric. After picking one of them, this person's other neighbor must be either Bob or Carla. Therefore, the total count is $$C_2^1\times C_2^1\times C_2^1\times P_2^2 = 16$$

Hence, the final answer is $12+16=\boxed{28}$.