We get very little information about the travel, but we may expect that it was arduous. It is also probable that they are returning along a similar path to the one Ammon took to find them, since the Limhites had already attempted to find Zarahemla and missed.
Upon arrival in Zarahemla, Limhi recognizes Mosiah's superior right to rule, and he and his people become subjects of Mosiah. This would be logical in that Zarahemla would have the greater population, the greater claim to rule, and the recognition that Zarahemla was saving the Limhites.