Not sure why the Danish and Greenlandic governments go to the WH to discuss with Vance. This is appearing weak.
As for how this is seen internally for Danes, at least in my part of the world the US admin has already achieved crackhead with a knife status. I suspect that trying the dog whisperer shtick (like Mamdani) will not be seen negatively.
You go to the King, the King does not go to you. The party that travels is the weaker one. Maybe that's childish but it is the standard power play even in daily life and business.