I partially agree with patrickmaher: don't wire to both the Ipac & TB at the same time.
If you want mouse buttons in windows or other apps (non-remappable), then I'd put a switch to flip the buttons between the mouse and the Ipac.
If you're just using mame, though, I'd do as patrickmaher said, but you can do the switch as above, too.
The reason you don't want the buttons wired to both the ipac and TB at the same time is just as you've seen; conflicting inputs. For another example: FE that can take a letter input to zoom to the next game starting with that letter, and a mouse click means start game. If you press a button that is wired to both the letter 'A' and the mouse click, the FE might jump to the first game starting with 'A' and start that game, or start the game you want and then jump, depending which action the FE sees first.