Glad you both managed to find a solution to this. For anyone else reading and curious, if you're using a recent version of LaunchBox and you've added Dolphin as an emulator, it should already come with a flag applied that will launch games in fullscreen. You can check this by going to Tools > Manage > Emulators, and seeing what is under the Default Command-Line Parameters for Dolphin. The full flag will be
-C Dolphin.Display.Fullscreen=True
For anyone using an older version where this flag isn't already applied, you can simply add it to your command line parameters, and that means any game launched through LaunchBox will load in Dolphin via fullscreen.
While we recommend this approach for ease of use, if you prefer there is an option in Dolphin under Graphics > General > Basic called "Start in Fullscreen". Selecting this will start any game from Dolphin in fullscreen mode and is basically what the flag is controlling when you launch via LaunchBox.
AstroBob's post in Dolphin Launch in Fullscreen? was marked as the answer