In Scotland at the time, there wasn't primogeniture at all. You got to be king by general acclimation -- you were king when everybody said you were king.

The previous king might nominate a successor, and it might be his son -- any son. And if the thanes didn't like it, they'd fight about it. ("Thane" was an Anglo-Saxon context that's not really appropriate to Scotland at the time, but they had something kinda parallel.)

Shakespeare hints at that, in an important scene were Mac expects to be named the heir. Shakespeare's audience would have understood that, because it had been roughly the same in England under the Saxons. (That was more than a half-millennium ago, but the history was well understood by the educated, using the same sources Shakespeare did.)

There was a problem with offspring in general. Shakespeare actually discussed that one, too, in King Lear. Properties could be divided, but not indefinitely, and it often caused fighting. It's what led to the clan system, which really evolved after the Norman invasion but hints of it lay earlier.

Thanks! Sounds a bit like the election of the German king in the Holy Roman Empire by the Great Electors. (It was customary for the king to semi-automatically become emperor.)

The problem was spare had to be good at fighting case heir kicked the bucket. Then you had to figure out how to keep spare from killing heir. Standard technique was to encourage them to go conquer someplace else. This was also an important driver of the crusades, which had the bonus of sending that heavily armed relative far away.

I was wondering that myself.

I answered in a parallel comment.