Historically, the ownership/control of the Canal wasn't much of an issue because the US was the only major power in the Western Hemisphere. The European powers used it, but it wasn't critical to them (Suez was more important). Here in WW, I'd expect Iberia to have concerns about the Canal being in US or Atlantean hands if there was only 1 canal, because Iberian relations with those countries have historically been tense at times and Iberia's west coast of the Americas possessions really need Iberia to have naval access to them.
As far as size goes, Panamax was an issue in US defense planning, as up until the Montana and Midway class ships, previous designs were all carefully sized to fit through the canal. For civilian shipping, no, it wasn't an issue during the 1930s.