ah! you might just need to set the dip switches in the game then.
Not all MAME games support cocktail mode. Let's pick one that we know does and experiment.
Galaga
Load it up, press the TAB key and you'll get a little popup menu. First make sure the screen orientation is correct for player 1 to be sitting at the P1 controls and the game works. If needed, use the video options from that popup menu and rotate the game until it's correct.
Then, there should be an option in that menu for dipswitches. Go into that, find the menu option for cocktail, and flip it on. You will have to reset the game (ctrl-F3 I think, or just exit it and come back), and that should take care of it.
You will have to do this on every game that support cocktail mode that you have in your list. It's a PITA, but you'll get to know your ROMs really well.