LAN Game mode isnt working on offline mode

I recently bought 2 DsT games(one for each Nintendo switch console) to play via LAN mode offline whit my brother and the server list doesn't show's up on LAN server's list.we tried via lan cable whit a router at offline mode whit no internet.We also tried connecting both consoles to a same hot spot on a phone whit internet and the server doe's shows up on LAN section but when the one isn't hosting attempts to join the game crashes or it joins in but the games shows all screen in purple color.So the LAN mode isn't working at all and we feeling like we spent money on a second game for nothing.we can only play it on 1 at split screen mode.