Question regarding the in-game lore status of Laithland

Two questions, really: is Konung Gudrod Ragnarsson supposed to be one of the many sons of Ragnar Lodbrok? And are Ivar Godrodsson/ Grunnhild his children?

Even though the Notes page does not list a family relationship between the two, I'm assuming that Godrod and Ivar are the attested founders of the Ui Imair clan, Gofraid of Lochlann and his son, Imair. AFAIK, the IRL Gofraid of Lochlann was never listed as one of the sons of Ragnar, but the fact that he's named "Ragnarsson" leads me to believe that (so far as the in-game lore is concerned), he is.

I'm mostly asking because I want to shag one of Ragnar's daughters, but if Grunnhild is his granddaughter, that would be fine too.

I'm not quite sure how it works in-game, but I think the following is correct, at least to specific sagas, though keep in mind that, despite my efforts, I'm not exactly a historian, or mythology-whizz.

Gudrod Ragnarsson is son of Ragnar Lothbrok, (or Lodbrok,) brother to Sigurd, Ivar (note that this is Ivar Ragnarsson, but more on that later on,) Halfdan and Bjorn. Furthermore, and briefly onto the second question, I couldn't find anything about a "Grunnhild," but there is Gunnhild Gormsdottir, widely recognised as Mother of Kings, daughter of Gorm the Old and thereby possibly granddaughter of Sigurd "Snake in the Eye" Ragnarsson, obviously the aforementioned son of Ragnar, which would mean that yes, Gunnhild is great great granddaughter of Ragnar Lothbrok, not related through Gudrod, but his brother.

Now,
Ivar Godrodsson, I confidently assume, is Ivar "the Boneless" Ragnarsson, king of Dublin, who furthermore, I think can obviously be linked to Imair (which even translates to Ivarr in Old Norse) Gofraidsson, who did, in fact, as you mentioned, found the Ui Imair with his father Gofraid Ragnallson, AKA Godrod Ragnarsson.

So, put simply Ivar "Ragnarsson," king of Dublin, is in fact not a son of Ragnar Lothbrok, but yes, as you thought, son of Godrod/Gofraid, who is brother to Sigurd, who are both sons of Ragnar, the latter of which is the father of Orm, father of Grunnhild.

SO AFTER A LOT OF RESEARCH FOR NOTHING IN PARTICULAR I CAN CONCLUDE:

Yes, Gudrod is the son of Ragnar Lothbrok.
Yes, Ivar Godrodsson is his child.
No, Grunnhild is not his child, but you were closer with granddaughter.

Gee golly.