It's as easy (and as hard) as this). In your "ini" folder you can make a ini file for any game and set individual mame settings for said game just like in your mame.ini (only include the ones you want to change). Only enable multi-mice on games that will need them.
I will say this though, your problem sounds unlikely. You do know that even with multi-mice turned on mame defaults mice-based inputs to use any and all mice and not just a specific one. In other words you have to remap the game, via ctrlr files to use "MOUSE_1" and not just "MOUSE". "MOUSE" or "JOYSTICK" refer to any and all mice and joysticks.... "MOUSE_1" or ect... refers to a specific device. You'll notice in the inputs menu for a lightgun game, even with "-lightgun" on that the inputs for movement default to "Gun_1" OR "Mouse X". The "gun_1" is fine, but "mouse x" refers to ALL mice.
Solution:
Scroll down to the section of your mame.ini that reads "RE INPUT AUTOMATIC ENABLE OPTIONS"
Now make the following adjustments: (not sure about your particular setup, so I'll ignore things like pedals and paddles)
paddle_device keyboard
adstick_device keyboard
pedal_device keyboard
dial_device mouse
trackball_device mouse
lightgun_device lightgun
positional_device joystick
mouse_device mouse
Now with the exception of maybe the joystick flag, NEVER turn on "mouse" or "lightgun" via ini or command line.... the setup I just gave you will automatically switch on and off those features depending upon the game ensuring that they don't interfere with each other. You can leave multi-mouse on, just make sure "mouse" is off. That should fix most of your issues.