Also a reminder that arcade games commonly shared a single set of controls, for example pacman. So player 2 actually uses player 1 inputs when it's their turn. There were also games that had distinct player controls such as tmnt or mortal kombat. It would help to specify the game your trying to play to determine if that plays any part in your issue.

So,
for me I find "my" solution" to use two joysticks (for my 2P games) without any problem ;-)

The DragonRise USB adapter has the option to use (connect) 12 buttons (plus 4 for the directions),
I use 6 "inputs" for the second player joystick from one DragonRice Joystick-Adapter.
Three free connections on the DragonRise circuit board, and three connections which are not used when playing (like P1 and P2 start-button) and the button 4 (not used in most games), so I have totally 6 "inputs" for the 2nd players joystick.
To connect a joystick (I use my 25 years old competion pro joystick) I solder a 9 pole D-sub plug on it, on the Arcade station also a D-sub rifle.
The second player has "only" 2 buttons he can use (plus 4 for the 4 directions) , but in my most 2 player games this is enough.
In the Mame inside menu I only have to press the wanted buttons on the usual way to learn the buttons for the second player (game by game).

For me it works, no issues with a second USB controller etc .... player one and player two are using the same hardware "controller", only different inputs from this ...

I hope it's clear what i mean ;-)

D-sub rifle (nine pole; 7 used: 6 for the buttons plus ground):
arcade-buchse.jpg

Plugged in Competions Pro:
arcade-joystick-9pol.jpg