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When wielded in both hands it’s a weapon that is two handed, so a two-handed weapon.

When I look at Power Attack, it differentiates between two-handed weapons and weapons wielded in two hands, though.

This bonus to damage is increased by half (+50%) if you are making an attack with a two-handed weapon, a one handed weapon using two hands, or a primary natural weapon that adds 1-1/2 times your Strength modifier on damage rolls.

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Wielding a Weapon Two-Handed: When you deal damage with a weapon that you are wielding two-handed, you add 1-1/2 times your Strength bonus (Strength penalties are not multiplied). You don't get this higher Strength bonus, however, when using a light weapon with two hands.

So, the longsword counts as light and also can’t benefit from two-handing.

Effortless lace only makes it light for certain feats and abilities, though.

the weapon is treated as a light melee weapon when determining whether it can be used with Weapon Finesse, as well as with any feat, spell, or special weapon ability that can be used in conjunction with light weapons.

Agile specifically forbids it.

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This modifier to damage is not increased for two-handed weapons, but is still reduced for off-hand weapons.

The longsword is a one handed weapon wielded in two hands, and not a two-handed weapon, which should work with Agile, assuming it still counts as a one-handed weapon while wielded in two hands.

I have a build that I came up with and wanted to see if it worked.

I have a Medium sized creature wielding a +1 longsword in two hands.

I then attach an effortless lace to the longsword, letting it be used with Weapon Finesse.

The effortless lace longsword is then enchanted with Agile.

Can I wield this longsword in two hands and get both DEX to hit and 1 1/2 DEX to damage, or do I only get DEX to damage?