[RPG] What defines a “willing target”

No. Nothing in the wand rules notes that anything about the spells stored in the wand changes. While the list of spells in the wands are all spells that can target other creatures, there is no reason why a wand cannot cast a spell of "personal" range on the person who can trigger the spell.

A feat or PrC is needed for the wand to behaved differently. Extending personal spells to others can be done through the Spellguard of Silverymoon PrC (Player's Guide to Faerûn).

This is a common problem - I always have players wanting to pick someone up and carry them along, or push them out of the way of a closing door, or hit them with a rope or something while they're falling or in the water near a ship, or trip them so a trap passes overhead, or disarm them of a magic gem they're holding when they just realized might melt their face off, or they need someone to stab them to activate their Kewl Blood Powerz (tm). And these actions all have the same root problem, which is that attack rolls/CMB checks aren't technically opposed, unlike skill checks and saves, so it's not clear how someone decides to fail the check.

RAW is silent on this, so let's try out common sense, as is our God-given right as GMs and players. Should it be a lot easier to hit/move/disarm/trip someone who's not resisting it? Yes, totally. Should it be automatic? No, certainly not - even if the person isn't resisting, there's sheer physics in play.

Here's how I usually rule.

First, the target decides whether to resist or not. If PC#1 comes lumbering towards PC#2, maybe he trusts him to bull rush/trip/stab/touch him and maybe he doesn't - in intrigue-rich games this is a nontrivial decision (he's reaching out to touch you while you're in melee... A Cure Light Wounds spell, or his long-awaited betrayal?). If they resist, normal rules apply.

Second, if they're the trusting sort, then if it's a to-hit roll I use flat-footed AC (touch and flat-footed if it's appropriate, like tossing a rope to someone). If it's vs. a check, like with 3.5e bull rush, that's harder. I normally play Pathfinder, where it's a little more straightforward, so I'll reverse-engineer from there.

In Pathfinder, there's the somewhat cleaner CMB/CMD mechanic that covers all combat maneuvers.

CMD = 10 + Base attack bonus + Strength modifier + Dexterity modifier + special size modifier + miscellaneous modifiers

Part of CMD is, in theory,"active opposition", because it's factoring in your BAB and STR and DEX, all of which are under your control. So in these cases I assume you can willingly fail the part that's in your control (BAB + Dex + Str), leaving CMD = 10 + special size modifier + miscellaneous modifiers.

IMO this strikes the right balance of "not automatic" and "not way super hard in an unrealistic way".

So for 3.5e, that means the person can't just fail the opposed check, but they don't have to roll it, they can just set a passive DC of 10 + relative size. So the wizard is going to have a tough time bull rushing his ogre buddy out of the swarm, while vice versa should be a cinch unless something goes really wrong.