I would not like to see that the events of the union with Sweden and the Kalmar Union has to happen when you are playing one of the powers. Remember, they all happened as results of who the kings choosed to marry their daughters to.
As for civil wars, they should only come as results of your actions as a king. The game is about having a chance to change history instead of just repeating it. Also, don't bother mentioning king names and such long after the start of the game. Because from what I have heard, the names are random for the comps and you can choose your own names for your dynasty
However, at starting dates like 1187, parts of Norway should probably be in revolt, giving King Sverre (whom also should be a good commander considering he never lost to his opponnents) a hard time gaining full supremacy.
For the starting year 1337, when the union between Norway and Sweden had already happened, it should still be a possibility of breaking loose from the union, pherhaps with the Bjarkøy dynasty under Vidkunn Erlingsson or if done later with the Sudrheim dynasty by Sigurd Hafthorsson or even by the Losna dynasty under Erlend Eindridesson or Eindride Erlendsson.
Considering the fact that Norwegian armies were only led by kings (except a few nobles on some occations), these kings should gain some advantages in command to compensate for the lack of generals.
Let us say that the first born son of Olaf III (whom I presume is the starting king) has some bonus command points, concidering that Olaf's son was Magnus Barefoot. Also when starting with King Sverre in 1187, he should be an exellent commander. But of course, one should be able to "build" the commander into becoming good. Pherhaps the title for a general could be Jarl in the Scandinavian countries (at least Norway and Sweden)...
Another thing, it should not be made insane impossible for Norway to go on a crusade and actually be in the holyland before two years have passed, concidering Sigurd Jorsalfare went on a crusade, and concidering Norway uses longboats (which are fast transports) up until ca. 1300. Of course, the crusades should be events that happen on the exact dates as they are declared by the popes. I would actually like to see the computer players play as historical as possible with you making most of the changed to the alternate history, and then pherhaps the actions you made cause some of the AI players that are affected by your actions to change their course. So pherhaps many historical correct events like for example those stibogis are mentioning can be used in lands not controlled by yourself, just to direct the AI players into following a realistic behaviour.
1070
Bergen founded by Olav Kyrre.
Ain't that up to Olav Kyrre to decide? And shouldn't it also be up to Olav Kyrre if that "Kyrre" nickname will be apropriate for his reign (Kyrre means the Peacefull). Afterall, starting in 1066 playing as Norway, you will be Olav III and therefore able to decide how his reign shall be.
What a terrible thing wouldn't it be if the civil wars could not be prevented, same dynasty fighting brothers against brothers. Well, it should pherhaps be in the settings for Norway before you start the game, civil war 1130 or not, and then birkebeiner (birchleg) rebellion in 1177- or not (thinking that it would be a little wierd with first a rebellion by Øyvind/Øystein Møyla and then by Sverre, pherhaps the rebellion by Møyla should then be just cut out in case there will be birkebeiner rebellions). However, unlike the civil war in Sweden, this will not be fought between different dynasties, but members of the same.
1349-1350
The Black Death in Norway
Reaches Bergen in 1349 and some other places but spreads trough the rest of the country during the next year.
People living in Norway down whit 70%
From 650 000-800 000 to 70 000-200 000
Followed whit many smaller plages.
Probably one of the only inevitable events, no matter what efforts the king may do. Though it was not that dramatic. More like 400 000 - 500 000 down to 200 000 - 250 000 or something

(well, almost that dramatic, let's just say they can cut half our population for that nasty event).