How did the Framers intend the Militia to execute the Laws of the Union in cases where state governments were in opposition?
Both Shays’ Rebellion and Whiskey Rebellion were confined to a portion of the population in a particular state, but would Congress then have the power, or dare to use it, to stick militia on a state government to coerce submission to federal law?
In practice federal law directly acts on a citizen of the United States, but nowadays federal laws seem to require state cooperation to enforce.
There’s no indication they did. In three states, a right to secede was expressly stated in ratifying, and the Tenth Amendment principle was said to be implicit in the unamended Constitution by prominent (Madison, Hamilton, Iredell, Pinckney, Cushing, Wilson, et al.) Federalists in at least eight states; in no state was that principle contradicted.
During the Secession Crisis, President Buchanan said secession was unconstitutional, but he had no power to prevent it. That latter was widely believed too.