Here is my revamp. I think that incorporates everyone's comments. Should this feat apply only to one weapon (as written) or to all three?
Two-Weapon Trip[General]
You are a master of the quarterstaff, double-axe or urgosh, able to use the weapon more effectively than others in combat.
Prerequisites: Weapon Proficiency with the chosen weapon, Weapon Focus with the chosen weapon, Two-Weapon Fighting, Dex 15, Bab +1
Benefit: You can make trip attacks with the chosen weapon. When you make trip attacks, make a melee touch attack against your target. You don’t provoke an attack of opportunity. If you are tripped during your own trip attempt, you can drop your chosen weapon to avoid being tripped.
Normal: Only weapons marked as Trip weapons or unarmed strikes can be used to make trip attacks.
Special: A fighter may select Two-Weapon Trip as one of his fighter bonus feats. You may take this feat more than once. Each time you must choose a different weapon from those listed above.