My comments in red, descriptions edited for relevance.
D&D 3/3.5 Trip
You can try to trip an opponent as an unarmed melee attack (this means a lvl 20 Ftr with no enhancements to ApR can make up to 4 trip attempts per round). You can only trip an opponent who is one size category larger than you, the same size, or smaller.

If you lose, the defender may immediately react and make a Strength check opposed by your Dexterity or Strength check to try to trip you. (I can see where this might be difficult to code, but I'd like to see it applied to the game version).
D&D 3/3.5 Improved Trip [General]
Prerequisites
Int 13, Combat Expertise.

Benefit
You also gain a +4 bonus on your Strength check to trip your opponent.

If you trip an opponent in melee combat, you immediately get a melee attack against that opponent as if you hadn’t used your attack for the trip attempt.
DDO Trip
Cooldown: 15 seconds (note that a D&D combat round is roughly 6 seconds, in which a lvl 20 Ftr can make FOUR (4) trip attempts if he desires)

Attacks/spells already started will complete, however.(This is bogus and should force a Concentration check)

Prone creatures are given a Balance skill check every 2 seconds to stand up early.(This is also bogus when compared to the cooldown of Trip)

Your character's size doesn't affect your chance to trip. (You need to implement proper size modifiers; if that means halflings have a more difficult time tripping things, good, that's how it's supposed to be. They're child sized)
DDO Improved Trip
Cooldown: 10 seconds (Slight improvement over the base Trip feat)
These simply don't work like they should. They should be changed to something more like

Trip
Cooldown: 6 seconds
Useage: Active
Prereq: None
An attack roll is made against the target. Like any melee special attack, it works with your combat flow and is queued to work on your next melee attack. Ideally you will time this so that it will work at your maximum attack bonus.
If it hits, it will do only a regular damage hit (will not produce offhand damage or glancing blows), and in addition attempt to trip the target.
The target then takes a Strength or Dexterity save (whichever is higher) against a DC of 10 + Strength modifier + related Enhancements + related item bonuses. Should the target fail its check, the target is tripped.
The target remains tripped for until it succeeds on the Balance check to get up, during which time it is rendered prone and may not move or attack. Prone targets suffer -4 AC. Attacks/spells already started require a Concentration check to continue with failure interrupting the action.
Prone creatures are given a Balance skill check every 3 seconds to stand up early. The DC on it is the same as the trip DC, but it uses the Balance skill rather then Strength or Dexterity.
Some creatures are immune to tripping, such as those that have no legs (like oozes) and those that naturally hover or levitate (such as mephits and ghosts). Red and purple named creatures are also immune.
Your character's size affects your chance to trip normally.
Has a normal duration when used against players.

Improved Trip
Cooldown: 2 seconds
Usage: Active
Prerequisite: Combat Expertise
Description
Improved Trip has a chance to trip the target, rendering it prone. Improved trip has a superior base DC (+4). This feat replaces Trip as an action.
Official in-game description: Using this attack, you may trip the target, rendering it prone for a longer time. Some creatures may be immune to this effect.
Notes:
An attack roll is made against the target. Like any melee special attack, it works with your combat flow and is queued to work on your next melee attack. Ideally you will time this so that it will work at your maximum attack bonus.
If it hits, it will do only a regular damage hit (will not produce offhand damage or glancing blows), and in addition attempt to trip the target.
The target then takes a Strength or Dexterity save (whichever is higher) against a DC of 14 + Strength modifier + related Enhancements + related item bonuses. Should the target fail its check, the target is tripped.
The target remains tripped until it succeeds on the Balance check to getup, during which time it is rendered prone and may not move or attack. Prone targets suffer -4 AC. Attacks/spells already started require a Concentration check to continue with failure interrupting the action.
Prone creatures are given a Balance skill check every 6 seconds to stand up early. The DC on it is the same as the trip DC, but it uses the Balance skill rather then Strength or Dexterity.
Some creatures are immune to tripping, such as those that have no legs (like oozes) and those that naturally hover or levitate (such as mephits and ghosts). Red and purple named creatures are also immune.
Your character's size affects your chance to trip normally.
Has a normal duration when used against players.