James Jacobs says it adds to the damage of the triggering attack (typically, the second claw that hits, though it varies by monster), which is also how the Two-Weapon Rend feat works, meaning that it does not apply DR again nor Power Attack again (nor Sneak Attack or on-hit effects like flaming), because it's just bonus damage on the attack.

The RAW doesn't specifically say.

As you note in your research, none of the rules related to hitting objects have any information about what to do if the object is attended.

That said, you can use existing rules to figure out a reasonable alternative. The rules for smashing an object that you link say:

An object's Armor Class is equal to 10 + its size modifier (see Table: Size and Armor Class of Objects) + its Dexterity modifier.

If you try to use the spell rusting grasp on someone's armor:

You may employ rusting grasp in combat with a successful melee touch attack. Rusting grasp used in this way instantaneously destroys 1d6 points of AC gained from metal armor (to the maximum amount of protection the armor offers) through corrosion.

You can similarly touch a weapon with rusting grasp:

Weapons in use by an opponent targeted by the spell are more difficult to grasp. You must succeed on a melee touch attack against the weapon. A metal weapon that is hit is destroyed. Striking at an opponent's weapon provokes an attack of opportunity. Also, you must touch the weapon and not the other way around.

It says that weapons are harder to grasp, but it doesn't actually give any rules for how you should determine the AC of the weapon.

With this in mind, one reasonable ruling would be to apply this rule to attacks against attended objects, but let the object use the attending character's Dex bonus instead of its own, as well as any other modifiers that the character has that apply to touch attacks, like deflection bonuses or a monk's Wisdom to AC. If you try to touch an attended weapon, you provoke an attack of opportunity. This means that it's a little bit harder to hit an object that a character is attending than it is to hit the character, since most objects are smaller than their users.

Another reasonable ruling would be to say that it's a Combat Maneuver, like any other. In this case, I'd say that touching an object that's being attended by another creature would work like Sunder. In this case, you'd simply make a CMB check against your opponent's CMD, provoking an AoO if you don't have Improved Sunder. The drawback of this approach is it means that it's basically impossible for casters to touch an object being attended by a creature except at very low levels, since the CMB of a caster goes up very slowly, but the CMD of most other creatures goes up very quickly.