I'll try to elaborate the idea a little bit. Maybe some modmaker will be interested...
This Royal Progress is something like the "Go on a foreign tour" decision, only this time the tour is not foreign.
1) You decide to go on the tour. Start preparations. The goal of the tour is decided and announced in the very beginning:
- long tour: all direct vassals
- medium tour (probably Iron Throne only): choice between a) Nearby lands: the Crownlands (dukes only), the Stormlands, the Riverlands; b) Journey North: the Vale, the North and the Wall (only if it is controlled by the Night's Watch and only if it is not under attack); c) Journey South (or maybe "along the coast" could be a better name): the Dorne, Oldtown (High Septon, the Citadel + maybe an exception can be made for House Hightower, since they're that important) and the Iron Isles; d) Jorney West: the Westerlands and the Reach (Highgarden). Obviously, only the kingdoms that are actually under the Iron Throne are visited (+the Wall).
- short tour: direct vassals (dukes and counts) in the capital kingdom only (Crownlands for the Iron Throne, other lands for independent kingdoms before conquest)
2) If a war starts during the preparations (or anything bad happens, like your ruler becomes incapable or pneumonic or something) - the tour is cancelled. There could be an event giving negative opinion modifiers to the people that were expecting the king (they don't like being neglected). + maybe you could send your wife or your brother, or your heir instead of you (like Jaehaerys sent Alysanne to the North). If this person is a good diplomat, the negative opinion modifier can be evaded. Or in the worst case this person could be imprisoned somewhere! (This event could happen to the King too - Defiance of Duskendale!) Or if this person is a claimant to the Throne he could plot against you and gain support for his faction.
3) Finally the tour starts. A regency begins. You decide who to take along with you (chose if you take your children with you - Robert did take Joffrey with him). Being at least 6 (or maybe 8) years old should be a requirement.
4) Events during the road.
- For travelling by sea they are almost the same as the current events for the foreign tour. Obviously, the sea route is used when the King travels to the Vale (Gulltown) and to the North (White Harbor) - and also when the King travels to the Dorne (no big roads there anyway), Oldtown and Iron Isles. The only difference is that the events should affect not only the king, but also his relatives.
- For travelling by land, as I've already mentioned, the obvious events are the attacks by fanatics / Poor Fellows. The Kingsguard can be involved.
- For dragonriders there probably should be an option to send your court away ahead of you and to fly on your dragon yourself. Or there could be an option to use the usual roads/ships anyway (in order to make a peaceful impression on your subjects or something like that).
5) Now, the King arrives at Winterfell (for example).
He meets the lord of the North and his family. Either he makes a good impression - or a bad one. Same goes for his wife. Here we have some analogue of the events of the "Introduce Heir to the realm" decision.
He can also meet the councillors of the local lord - especially if they are dukes. I doubt that he would meet random lowborn courtiers, though.
If the King has taken his children along with him, his children meet the children of the local ruler (or maybe all the children that are currently in Winterfell). Friendships/rivalries/love. Parents can be involved (or not) - like when Robert, Cercei and Eddard had to solve the conflict between their children.
If a relative/friend/rival/lover of the king (or the queen, or whoever goes travelling with the king) lives at the local court, there could be events dealing with that.
- The ruler can be persuaded to leave a hostile faction or to join the loyalists. (Or he can leave the loyalists if he's insulted somehow.)
- The Defiance of Duskendale scenario:
awoiaf.westeros.org/index.php/Defiance_of_Duskendale- probably there should be not only a way to capture the King or his family members, like in Duskendale, but also to kill one of them.
