The easiest answer to make here is that Theodore Roosevelt did both the best job and the worst job of respecting the job of the president as laid out in the Constitution. This is because different people have different views of what constitutes respecting the job of the presidency.
To a liberal, Theodore Roosevelt probably did the best job of respecting the presidency. It was under Roosevelt that the federal government first started to act in ways that progressives would have approved of. The government started to act aggressively to do things like reducing the power of monopolies and making sure that companies were not able to abuse consumers or workers. Roosevelt helped to push the Congress to do things like this. In doing so, he was respecting his duty to recommend measures to Congress. In doing things like this, Roosevelt was also taking care to enforce the laws of the United States. He was making sure that he used things like the Sherman Antitrust Act in ways that they were meant to be used. He did not just use the laws to help the rich as had been done in the past.
However, a conservative might argue that Roosevelt did the worst job of respecting the presidency. Conservatives would argue that it was under Roosevelt that the federal government started to move away from its proper role under the Constitution. They would argue that Roosevelt allowed (and even encouraged) the government to start to intrude on the US economy and society. In doing so, he failed to faithfully uphold the Constitution.
This comes down to a disagreement about what it means to truly respect the job. Does it mean to push the government to do more or does it mean to push for a more limited government.