I finally figured it out, and in case anyone needs to know for future reference:
Option 1: Go into "Slot Devices" by pressing TAB to get into the MAME config menu and choose "Joy" under "ctrl2" - This is not set by default.
Option 2: Add -ctrl2 joy to your command line in emulators.cfg - This will force a controller to put put into controller port 2. So for example, my command line for Astrocade looks like this:
lr-mess-astrocade = "/home/pi/RetroPie-Setup/scriptmodules/run_mess.sh /opt/retropie/emulators/retroarch/bin/retroarch /opt/retropie/libretrocores/lr-mess/mess_libretro.so /opt/retropie/configs/astrocade/retroarch.cfg astrocde /home/pi/RetroPie/BIOS -ctrl2 joy -cart %ROM%"