Two-thirds of the group had met up at Hope's father's place by the start of the week, but they didn't get to rest long before PSICOM caught up with them and the game transitioned to focus on the remaining one-third of Sazh and Vanille. Massive stuff goes down with them involving Dajh, Sazh's son, and the events surrounding the boy becoming a l'Cie. However, Sazh and Vanille ended up captured. The rest of the team learned of this and went to rescue them!
Direct video links:
Tactical Regrouping—Final Fantasy XIII First Playthrough Ep. 26 - https://youtu.be/WaekxCkS6r4
Chocobo's at Nautilus Park—Final Fantasy XIII First Playthrough Ep. 27 - https://youtu.be/snp9R7hKf58
Dajh's Focus Fulfilled—Final Fantasy XIII First Playthrough Ep. 28 - https://youtu.be/IeDthIBT-Cs
Flying into a Trap!—Final Fantasy XIII First Playthrough Ep. 29 - https://youtu.be/fh4NFETJaow
This is less an infiltration and more an assault...—Final Fantasy XIII First Playthrough Ep. 30 - https://youtu.be/ISJ_phXu3ps