There is no way to currently progress the Rose Thorn questline when you are in the caravan as there is no place to sleep or pass time.
When I tried it I thought it was completely broken, so I used the Unstuck feature and continued playing. I'd gotten near the end of the game by the time events started automatically playing out, and it automatically teleported me all the way back to the south end of the map. Timed events play out no matter where you physically are, it's wild.