Shock is right for the most part, as your symptoms support that mame is seeing the mouse type devices as separate inputs.
However, depending on which version of mame and windows you're running, another fix might be easier. Current mame has a -multimouse option; make sure it is disabled (the default). When disabled, all mouse type devices are grouped together (much like you are seeing in windows & MALA). However, older versions of mame didn't have the option and forced multiple mouse support.
FWIW, I love that mame has true multiple mouse support (IOW can see each mouse individually). I prefer having the mice separate (even with the remap "hassle"; hint use ctrlr files), but with virtually zero other applications out there that can do the same, it seems many people don't find the multiple mouse support "intuitive". (IMO, it's not "intuitive" because they have learned "there can be only one mouse"; while they have no problem with each gamepad seen independently.)