@High Seas,
There are two issues with respect to Canada's claims to the inland northwest passage (the sea lanes above the Laborador Strait). The first has to do with their claim that it is their national waters. The U.S. recognizes their claims only out to 12 miles from the shoreline - the generally accepted international limit.
The second has to do with the "right of innocent passage" of non hostile ships through recognized international sea lanes - even those that may lie within territorial waters. (The Bahamas straits off the coast of Miami lie entirely within U.S. and Bahamian waters - however they are a main international waterway, traversed by ships of all nations without any requirement for permission or even prior notice). At one point in the 1980s some factions in the Canadian government were demanding prior notification of any U.S, Navy operations even in the offshore areas of the Labrador Straits, The U.S. refused flatly to comply or consider the matter, and I believe that aspect of the issue has since died down.
An underlying issue there was our covert submarine operations there and in Arctic waters.
There are many disputed issues such as these in the world. Indonesia claims the Lomboc Straits near the island of Bali as national waters and refuses even the right of innocent passage. The U.S. (and other maratime nations - Australia & Canada included) routinely make a point of using these Straits (one of the few navigable routes through the island chain to the South Pacific) - often with Naval vessels, just to prevent any taxit recognition to develop. (I traversed these straits at least 10 times.)
At the end of the day, international law in these areas is simply what you are able to enforce and what others accept, either formally or tacitly.