I just checked the dots I have for Both Sides the Tweed and it is most definitely in Dm, though it is a modal Dm rather than a "classical" Dm

However, the last two bars contain the notes G E C |D which would suggest to me a chord sequence of Am7 to Dm. If you were following the harmonic rules in theory books such as those published by the Associated Board then you would make the C into a C# which would give you a chord sequence of A7 to Dm or you could even follow Renaissance (and to some extent Baroque) practice of making the final chord a major chord as well even though the mode suggests a minor chord.

So possibly it is the two minor chords that makes the final cadence feel as if it is not quite resolved as our ears have got used to a dominant seventh to tonic final cadence.

On way round this, I have seen suggested is to harmonise the final cadence with a VII to Im sequence, in this case C to Dm

Just some thoughts based on bits and pieces I've picked up over the years.