Yes, it's 1/4

You ask "when the resistance applies". The PHB answers that:

Resistance and then vulnerability are applied after all other modifiers to damage.

Obviously this is before you take damage. As you mentioned yourself, the wording is very clear

half the damage you take from the attack.

If you are unsure about what is the "damage taken", it's defined in the Damage and Healing subsection:

Whenever a creature takes damage, that damage is subtracted from its Hit Points.

This means the "damage you take" is exactly how many Hit Points you reduced, i.e., after the resistance was applied.

When you want to grab a creature or wrestle with it, you can use the Attack action to make a special melee attack, a grapple. (PHB p.195, "Grappling"

Using the Attack action, you can make a special melee attack to shove a creature.... (PHB p.195, "Shoving a Creature")

From these we see that both grapple and shove are a lowercase-a-attack, matching the wording of the Paladin's feature. (And they require the Attack action, in particular.)

The disarm's a different beast: either you're a battlemaster, your GM's using a houserule for disarming or they're using the DMG's optional rule.

• If it's the houserule, you need the GM to rule for you.

• If you're a battlemaster, the maneuver specifies that this occurs as part of any weapon attack.

• If it's the DMG option, consider its wording: "A creature can use a weapon attack to knock a weapon or another item from a target's grasp. (DMG p.271, "Disarm")"

So the battlemaster or the DMG disarm again requires an attack, suppressing the Paladin feature. (Note, though, these do not require the Attack action. The battlemaster's disarm might come as a bonus action attack (Flurry of Blows or off-hand attack, for instance); the DMG disarm is listed as an "action option" and purportedly must be an action taken in and of itself.)