The first source you link to is an index-card abstract; the second source (the Viknabok) has much more extensive extracts from the probate.
"Myndig" means "of age"; the fact that Karen is not designated as such simply means she was still a minor (just like Isak). This is confirmed by the fact that she was given a guardian (just like Isak). She was in fact an heir, and there is nothing here to indicate that she was illegitimate.
My main concern here is that the math doesn't work out. After the widow got her half of the net estate, the amount due to be given to the kids was about 36 daler. As was common in Norway back then, sons got a full share and daughters a half share. The son's share (broderlod) was calculated at slightly more than 7 daler, and the daughter's half share at slightly more than 3.5 daler. This adds up to 36 daler if you have 4 sons and 2 daughters - but per the probate there were only 3 sons and 2 daughters. So it looks like the kids got cheated out of a bit of their inheritance (sorry, this is the retired accountant in me taking over).