Hi Rampy,
Sorry, I didn't catch this thread earlier.
Start with some analog+ input info.
"sysmouse" is all mice inputs pooled into one mouse (only mouse standard mame uses). "mouse 1", "mouse 2", etc are first USB mouse, second USB mouse, etc (notice all are USB mice). The "sysmouse" includes all USB mice.
mame (and thus mame:analog+), however, treats lightgun inputs differently than normal mice inputs. Basically this means analog+ is forced to use only the sysmouse for lightgun inputs, too.

I just got my actlab lightgun to
night (8:00 PM, "knock, knock", "Hello", "UPS delievery"

), so I can start testing some lightgun changes for analog+.
Now looking at your assumptions.
ASSUMPTION 1: Analog Mame + and win98 support two trackballs (mices) as two distinct cursors/players
More like: "If coded to do so, and the (two) USB mice have good drivers, an application in win98 with directX 8 can draw it's own (two) distinct cursors/players."
Analog+ is one such application for trackball and dial mame type inputs, but not for lightgun mame type inputs (mame type is different than hardwaretype). Win98 still only draws it's one sysmouse cursor, but don't worry about that (I think).
ASSUMPTION 2: Dueling USB ACTLABs light guns don't work because
a. Driver doesn't support it
b. Mame support couldn't differentiate between the two drivers
(? ?) as they are the same...or looks the same as one (system?) mouse cursor thingie or something...
Don't think a) is the problem. b) is partially true, though. And I would think there needs to be a part "c): vga box causes some problems if two are in series," maybe.
I might be able to make some edits to analog+ and "fix" b) if I play around enough, err, I mean
don't play too much while testing my coding.

Now your test results
I tried to do the "remove the serial port until it boots entirely" but then the non actlabs gun doesn't initialize/work ...
The USB actlabs gun doesn't work?

Might happen if the USB gun "claims" "winmouse 1", and then the serial gun, after serial ports startup, claims "winmouse 1" without changing USB gun to "winmouse 2". (note, "winmouse 1" not the same as analog+ "mouse 1")
They seem to fight over the same cursor but register different hits (blue and red in police trainer for example)
The "fighting cursor" is probably due to mame's (and thus analog+) method of reading lightgun type inputs from sysmouse (as mentioned before).
Mame (and thus Analog+) treat the trigger as normal buttons, however, so analog+ still sends the correct button input to the game, resulting in the different hits.
If I could just map lightgun b. to player 1 I'd be in business...
I assume you have lightgun a to player 2, and you want lightgun b (but not lightgun a) to player 1? And player 2 works better than player 1? Hmm... Is player 2 using the USB or the serial gun?
I'll hook up my gun and get back to you with my test results (I only have one, though. Maybe I should get a second just to test.)