The Masorete בן נפתלי—whoנפתלי, who we don’t follow—addedfollow, added the dagesh, likely as an easier way to separate the נ from the preceding ן.
בן אשר—whoאשר, who we do follow—wasfollow, was usually more conservative than בן נפתלי, and he didn’t add this dagesh to his codices.
So our מנהג—which, in this case, is almost certainly the older one—is not to have a dageshDagesh in this נ. Instead, we make a small but clear separation between the two words, as you mentioned in the last sentence of your question.
However, if a בעל קורא were to find this difficult for some reason, and were better able to pronounce the phrase according to the dagesh of בן נפתלי, it seems that he shouldn’t be corrected for it, as long as he makes the dagesh very clear on the second נ, and the LACK of dagesh very clear on the first ן.