Oh indeed there are going to be tensions. Confederate vets would be embraced by most of the populace but still they'd have to follow the law as set down by the Union or they'd be considered outlaws, just as any other law breaker would. I'm sure there was brawls, stabbings, shootings but they would be dealt with harshly. The army used a lot of ex Texas rangers and other lawmen that had not worn a Confederate uniform to keep the peace at this time. They might have even turned to ex Confederates though it's still early after the war. 

[@User], is it ok with the GM to have more than one character?