Janow explains while they're there that she'll need to see if Raafi has the components she'll need and it'll be a couple of days before she's done even if he does, and then they can check out the site and Raafi's supplies - she'll have to make a couple of substitutions from how she normally does things but yes, she can do it; the next step is to sketch out her plan, which she starts on, explaining to Uamok and her mates the general idea of what she's doing while she does.
It takes three days to complete the rune circle, and another for Janow to attune a new divining rod to this plane so that they can get back and forth. Raafi does a couple more classes, but spends most of his time with Rannura and Cochik, showing them around town; he finally gets around to seeing the males' troupe perform at the theater, and Cochik plays to an interested crowd the following night, and Rannura and Raafi rearrange things in his portable hole to accommodate a cache of canned spren to tide Uamok and her mates over until they can get a breeding stock of spren established in Oerth, and then with all the loose ends tied up, they can make the jump back.
They land in the deep desert, which Raafi warned them to expect and warded them against he heat of beforehand; he takes the rescue party and one of Uamok's mates in the first teleport to the palace, so as not to overly alarm the guards, and is back in less than ten minutes for the rest of the group, depositing them in a wide courtyard surrounded by sandstone walls with cloth sails hung above to offer shade; various workstations are set up around the edges of the space - the stablehand brushing down horses at one of them has a bad few moments when the horse he's working on panics at Uamok's appearance - but there's plenty of room to maneuver in the middle, and only a few armed guards watching them. "They've sent someone to let the prince know we're here, I expect he'll be out in a few minutes."