Hey Brad,
Could you elaborate a bit? You have Arcade controls -> PSX Pad -> USB Adapter -> MAME? Or is it Arcade -> PSX Pad -> DC Adapter -> Dreamcast? I guess I'm just confused.
In anycase, there are known problems with wiring them up console pads and arcade controllers simultaneously, even if one is powered off. Would this apply?
If you're using a USB adapter do you know which one it is? Certain PSX USB adapters have some inherent lag to them, others are okay.