It's hard to say how tough Reconstruction could become realistically, but many Radical Republicans supported trying southern leaders, confiscating the land of planters and redistributing them to former slaves and poor whites, maintaining the disenfranchisement of anyone who had anything to do with the confederate government or military, and generally doubling down on the rights of freedmen and their organizations. In OTL you had the Battle of Canal Street in New Orleans in 1874. Any of the Radical policies being put into effect would lead to more events like that. In the worst case scenario, you could see Redeemer militias seize control of a state government and declare its independence from the US. It would be a civil war within a state or states, pitting Republicans and freedmen backed up by federal troops against Democrats and Confederate veteran freikorps.
To get another conflict you need a level of resentment among ex-Confederates that didn't exist IOTL, especially after 1877. To get that, Reconstruction needs to last indefinitely, be more radical, and be backed up fully by the US government. None of those are likely. In all likelihood, if southern nationalists march on a state capital and seize control, moderates in the federal government will see the "error" of policy in the south and pressure the leadership to back down, if they don't do something stupid like declare independence.