The United States didn’t invade anyone. They put down an insurrection.
Most of the insurrection took place on the territory of the United States. Of course the insurection had naval forces and privateers too, and went to other countries. Vermont was invaded from Canada.
For several years, the matter of states rights were argued
in the legislature before the war started. Military installations in the South were set up to enforce the collection of tariffs. There were other issues involved in states rights than slavery.