We study theoretically the return probability experiment, which is used to measure the dephasing time T-2*, in a double quantum dot (DQD) in semiconducting carbon nanotubes with spin-orbit coupling and disorder-induced valley mixing. Dephasing is due to hyperfine interaction with the spins of the C-13 nuclei. Due to the valley and spin degrees of freedom, four bounded states exist for any given longitudinal mode in the quantum dot. At zero magnetic field, the spin-orbit coupling and the valley mixing split those four states into two Kramers doublets. The valley-mixing term for a given dot is determined by the intradot disorder; this leads to (i) states in the Kramers doublets belonging to different dots being different, and (ii) nonzero interdot tunneling amplitudes between states belonging to different doublets. We show that these amplitudes give rise to new avoided crossings, as a function of detuning, in the relevant two-particle spectrum: mixing and crossings of the two electrons in one-dot states (0,2) with the one electron in each dot configuration (1,1). In contrast to the clean system, sequences of different Landau-Zener processes affect the separation and joining stages of each single-shot measurement and, even in a spin-orbit-dominated situation, they affect the outcome of the measurement in a way that strongly depends on the initial state. We find that a well-defined return probability experiment is realized when, at each single-shot cycle, the (0,2) ground state is prepared. In this case, the probability to return to the (0,2) ground state remains unchanged, but the valley mixing increases the saturation value of the measured return probability. Finally, we study the effect of the valley mixing in the high magnetic field limit; for a parallel magnetic field, the predictions coincide with these for DQDs in clean nanotubes, whereas the disorder effect is always relevant when the magnetic field is perpendicular to the nanotube axis.