You are mixing up the issues.
The "Gulf of America" quip is prologue to discussions with Mexico about their trade, drug and human trafficking, and border security relationship. It's a rather tidy way of reminding Mexico how much they rely on the US and just how fair the US is about tolerating Mexico's shortcomings in their relationship.
The Canada comments were purposed differently. Trump had a problem with Trudeau as someone who was offside with most of his agenda. To some degree, demeaning him as a state governor was a way of reminding Trudeau he's the tail, not the dog. Trade issues with Canada are not as substantial as with Mexico, but by inviting Canada into the conversation first, it gives Canada a chance to control the agenda of any reworking, as whatever is worked out with Canada, the Mexicans will simply have to accept. Inviting Canada to see the benefits of joining the US isn't/wasn't a joke, but that gambit was again, laid out to bait the Liberals into exposing themselves as the enemies of our greatest trading and geopolitical partner and open the door to the Conservatives to brand themselves as well aligned with our greatest ally and partner. And, lo and behold, it seems to have had some effect.
Greenland is different again. Greenland is a serious business and geopolitical proposal. Denmark may not bite, but at the right price they ought to. The resources of Greenland would be much more effectively developed under American stewardship. Control of Greenland allows the US to install military security that the Danes never could (or would). Such a deal, at the right price, would be good for everyone. Denmark might even negotiate a NATO contribution holiday to offset some/all of the purchase price. That would resolve several issues at once. However, just because something is a good idea doesn't mean it will happen. It will be up to Denmark completely, but don't be surprised if they act all offended and give a "no at any price" response that they will be put under a lot of pressure to live up to their NATO commitments, which they currently do not.
None of these initiatives are a challenge to the sovereignty of any of the 3 countries. Only morons entertain that thought. However, in a world of autonomous, sovereign nations there are differences in bargaining power when it comes to national relationships. Little dogs can act like big dogs, but generally speaking such countries end up looking like rogue, unreliable and unreasonable geopolitical and trade partners, and end up on the outside looking in at productive trade and military alliances. The trick is to know who you are, know your strengths and weaknesses, and capitalize on your strengths so that you are perceived as a VALUED partner, rather than insisting that you are an EQUAL partner (when you aren't).