Not that we're probably going to come into this in my next session (we totally will, please help), but has this been resolved and I just missed it?
Other than that the check should be DC 12, I'm not sure where the issue is.
If the hero succeeds using his Insight skill in the challenge, he gets the sense that Shealis will consider giving them the case because learning its secrets helps the Shahalesti too. Depending on how you play skill challenges, you can give the player the information and he can roleplay it in a conversation, or you can just tell the player that his hero has this incredible flash of insight and tailors his argument around something that Shealis could accept.
The hero also gets a vibe that she will not respond to threats and intimidation and that using any Intimidation on her will fail. Of course, if they already used Intimidation on her, they already know that part.
Consider that a social skill challenge is run from the hero's perspective, but its resolution is from the target's point of view. The result may not be the hero's expectation, but will advance the story. The party wants to gain physical possession of the case, so the challenge is the heroes' attempt to secure it and their arguments fall along that line. Shealis has a duty to not do that, but will listen to the party as they try to wheedle it from her, and she sees a few intelligent nuggets in their arguments. In the end, she offers a bargain where both sides come out as winners --- She keeps the case, but Lyceum gets involved in its investigation.
Just because Shealis places conditions on having the case in Shahalesti control at the end does not mean that the Insight is invalid --- the hero thought that his argument was good and it was, just not in the way he thought. The check was just one of 8 that helped her understand that Lyceum may be helpful in deciphering the contents. That is the important part of this challenge.
About the map to the hideout: If the party wins without a fight, sometime during the aftermath of the challenge, Shealis goes to the kitchenette and offers a drink so they can talk more about the Ragesian threat and the party's adventures thus far (she is an ally at this point), and the map is just sitting there for anyone to examine (no DC needed. Shealis has dropped her guard). The hero can just glance at it and gain the information he needs to find the hideout's location without any roll. If the hero picks it up then roll a DC 12 Thievery to tuck it away before she turns around. If the scroll is taken, her anger may be a late discovery after the party has left (she discovers the map missing), or she can make a DC 20 Perception check while they are talking to notice that it is absent. She'll be angry at the heroes, but she has made a deal and won't break it. Remember that she is herself a spy and stealing stuff is something spies do. As long as she is convinced she is still winning, she will stick to her bargain.
Getting the case to Lyceum: One way the case can be returned to Lyceum is through Shalosha. She can receive the case from Clathan while the heroes are running around in the Fire Forest and brings it to the council in Adventure 3 with a note from the wizard that says he thinks it is best to let Lyceum have it. He also mentions Shealis' thanks to the heroes for their help. Katrina will be impressed when the Shahalesti princess mentions the party in front of the council.