Double-peaked narrow emission lines in active galactic nucleus (AGN) spectra can be produced by AGN outflows, rotation, or dual AGNs, which are AGN pairs in ongoing galaxy mergers. Consequently, double-peaked narrow AGN emission lines are useful tracers of the coevolution of galaxies and their supermassive black holes, as driven by AGN feedback and AGN fueling. We investigate this concept further with follow-up optical longslit observations of a sample of 95 Sloan Digital Sky Survey (SDSS) galaxies that have double-peaked narrow AGN emission lines. Based on a kinematic analysis of the longslit spectra, we confirm previous work that finds that the majority of double-peaked narrow AGN emission lines are associated with outflows. We also find that eight of the galaxies have companion galaxies with line-of-sight velocity separations <500 km s-1 and physical separations <30 kpc. Since we find evidence of AGNs in both galaxies, all eight of these systems are compelling dual AGN candidates. Galaxies with double-peaked narrow AGN emission lines occur in such galaxy mergers at least twice as often as typical active galaxies. Finally, we conclude that at least 3% of SDSS galaxies with double-peaked narrow AGN emission lines are found in galaxy mergers where both galaxies are resolved in SDSS imaging.