We present a theoretical model to investigate double-core-hole-state formation in molecules through sequential absorption of two x-ray photons from a femtosecond laser pulse. A complete time-dependent quantum description taking into account x-ray absorption and nuclear dynamics explicitly and Auger decay phenomenologically is established within the local approximation. Using this model, we assess the impact of the nuclear dynamics on double-core photoionization processes in the case of the carbon monoxide molecule. We show that sequential absorption of two x-ray photons modifies significantly the vibrational distribution of the photoelectron spectra of the double-core-hole states compared to direct single x-ray photon absorption. Depending on the shape of the potential energy curves involved in the sequential absorption processes, lower or higher vibrational levels may be favored. Furthermore, in the case where the final state is dissociative, the electron spectrum is further broaden and blue-shifted in the two-photon process.