Alright, so I did some more investigating.
It appears that the issue is that Player 2 always goes looking for a controller and button mapping, and will always attempt to assume control of Player 1's HitBox if no controller is found for Player 2. Keyboards do not appear to be a fix because SkullGirls allows for GamePad / Keyboard dual binding.
So in other words, even if you assign a keyboard to Player 2, Player 2 will default to the gamepad button mappings instead. There is no way to unbind the gamepad mappings as far as I can tell. Being able to do this would instantly fix the problem.
Here's a video that demonstrates what is going on and that the issue is basically a "Half-Life 1 input scripting" problem.
0:18 Only the PS4 Hitbox is plugged in. It is assigned to
Player 1. The controls are seemingly mirrored. Note that the button mappings
are identical for both players.
1:21 A DualShock 4 is plugged in off camera and is assigned to
Player 2. Note that the mirroring issue is instantly fixed. Note that the button mappings
are still identical for both players, yet the mirroring issue is no longer present. I then reconfigure my controls for
Player 1.
2:48 The controls for both players are reverted to their default values. I then exit the game.
3:21 The game is restarted. The DualShock 4 is assigned to
Player 1. The PS4 Hitbox is assigned to
Player 2. Player 2's controls are then configured to be in "Liam style",
with the kick buttons on the top and punch buttons on the bottom. Take notice of this. I then exit the game.
4:47 The game is restarted. The DualShock 4 is assigned to
Player 2 this time, and the PS4 Hitbox is assigned to
Player 1. Player 1's controls are then configured to be in Street Fighter 2 style, with the punch buttons on the top and kick buttons on the bottom. Take notice of this. I then exit the game and disconnect the DualShock 4.
5:44 The game is restarted with
only the PS4 Hitbox connected. It is then assigned to Player 1. At the options screen, take note of how Player 1 and Player 2's controls are seemingly mirrored, but
notice that the bindings for the attack buttons still differ. I then enter the training room.
At this point, while my directional movements are mirrored -- because the
movement bindings are the same for both players -- my attacks are not! I am pressing 1 button each time, but activating 2 different commands! Essentially, there are two issues at play here:
SkullGirls allows the same controller to be assigned to both players, and there is no way to completely unbind Player 2.
The former problem doesn't seem to exist with other controllers, so this is likely the fault of the Hitbox. However, the fact that SkullGirls does not permit anyway to unbind Player 2's controls is the fault of the game.
TLDR: Provide an option to completely unbind _ALL_ of Player 2's inputs or disable Player 2 entirely. I am not aware of any -unbindall command like in Half-Life 1.
