The entire purpose of Dany's story in the books is to show that she must choose between doing what is good for her people and what she wants to do. And whether she should enforce rule with fear and violence or by political compromise. I don't think she ever expresses a desire to not be queen (though she dislikes many queenly responsibilities), her internal conflict is about what a queen should do.
As it stands, the books have Dany currently rejecting political compromise (in the probably false belief that her husband is trying to poison her) and fleeing on her dragon (the same as in the show). The show has a similar narrative for Dany, but it's not stongly enforced by a fuck ton of chapters that don't really go anywhere and a lot of readers find boring.
This is why Sam's line is interesting. It mimics the books' narrative that Dany must choose between what a Targaryan Queen should do (rule by fire and blood), and what is good for the people she rules over. I don't think it should read literally - that Dany should give up her crown for Jon - but rather whether being queen is more important to her than saving the people.
I suspect Jaime's trial ends with him being forced to take the black. Possibly becoming Lord Commander, since Jon has left and Dolorous Ed is not exactly a general. Otherwise, I don't see how Jaime can be useful. He has no army and can't fight anymore, so he needs something to do until they retreat to King's Landing for the final showdown (by which I mean the Cleganebowl).
I though the episode was alright. It was mostly predictable, but at least it let us know where everyone was, what was happening and what the character's relationships are with each other. The way it mirrors LOTS of the scenes from episode 1 is clever, and makes it a lot more interesting than just "new series first-needs a recap in case viewers forgot stuff".
Oh, and I think D&D were right to cut fAegon. It's long and complicated, and it relies on a huge amount of history that could never fit in the show. His story sounds dodgy as fuck even in the books, which is why he's almost certainly a Blackfyre fake.
The idea that fAegon or "Aegon Strickland" will be introduced now is crazy.