Sure, but landing safely when Rego-jumping is Quickness-Encumbrance, not Finesse.
An animated corpse swinging a blade uses its weapon skill, not Finesse.
Baking bread in a magically hot oven is Craft:Baking, not Finesse.
While it's not canonical, I'd say it's reasonable that a magical crossbow that shoots mundane bolts very powerfully ("Vilano style") is wielded with a crossbow skill, not Finesse.
I don't think I'm twisting any rule here. As Tellus pointed out, the magus is attacking with his weapon skill. The spell is not being used to attack, but just to add push to the magus push. If I Rego your image two paces to the side of you, and you are dancing, the image dances based on your Dancing skill, not on my Finesse.

The ability to move metal is surely ReTe. But the ability to move Terram in response to your physical movements rather than your using Finesse to move the gauntlet is something very tricky, that you once again made up. It is totally reasonable for a magus to concentrate on how he wants the gauntlet to move using ReTe; for simple movements I'd happily handwave concentration and just assume it's effortless! It is not at all the same thing to have a ReTe effect that moves a Gauntlet without the magus having to concentrate at all, based solely on subtle hand and arm and body movements. This is a very tricky effect. It's not at all in the spell guidelines, or implied by them. It's utterly different from the norm.
That's the issue I was mentioning, and that we are discussing in the Sword of Damocles thread, here. Please contribute to it!

ReTe lets a magus move Terram. There's a spell (maybe a guideline?) that lets a magus move Terram around as would a person with Str 5. There's nothing at all that suggests that a magus using this guideline can move something arbitrary such that it acts on something else as though it were a person with Str 5.
Well, there's a spell (the Unseen Porter), plus a separate guideline for a different effect (the Hermetic Generans), both assuming that unmodified ReTe can manipulate stuff like a Str+5 person can. Obviously, some discretion is required in such a choice. ReTe can, without modifiers, move much more than a Strength +5 person can move, in certain instances (e.g. when moving, however slowly, a base individual of dirt, mud, or clay -- 10 cubic paces!).

The cheap "natural movement" guideline you chose for all the possible hand movements of a gauntlet does not strike me as the intent of natural movement. I don't have the guidelines here, so am not sure whether this is closer to the mark than the next higher one.
This is definitely a judgement call, but pushing more strongly (but still with a human force) something that is already pushed by a person, seems to me as "natural" as it gets without being so natural that it happens on its own, without magic. This is the criterion we use in our troupe:
If it's the classic "elephant in the room", something that is so obvious that it's immediately recognized as "unnatural" even by someone that's not paying close attention, it's highly unnatural. E.g. a box floating around on its own.
If it's something that may escape a casual glance, but will be seen as "unnatural" by someone paying close attention, it's slightly unnatural. E.g. a glass very slowly sliding across a table, a wheel that keeps spinning indefinitely without anyone turning it.
If it's something that will keep even a persistent observer in doubt about whether he's seeing anything "unnatural", then it's natural. E.g. something pushed by a human that moves as if pushed by a stronger human, a lock that unlocks or jams, a door that slowly swings or open or shut.

By the way, learning how to use a force multiplying gauntlet of this kind is itself tricky! This itself might deserve its own skill. After all, there is absolutely no magic (Corpus!) here to help out.
This is something I do not understand. Learning how to use servo-assisted steering was completely effortless and virtually instantaneous for every driver I've known.

Also, since there is no Corpus, the magus is likely to get injured very, very quickly from this heavy gauntlet chafing, yanking, jerking at his hands.
If you read the description of the spell, you'd see that it's impossible for the gauntlet to exert more than the slightest pressure on the hand, because that slightest pressure will make it move so as to ease that pressure. It's like having a host of bodyguards that push the crowds away from you when you walk in a crowded place. It certainly does not require you to re-learn walking, nor are you jostled by the bodyguards.

Also, the ReTe cast only on the gauntlet only holds up the Gauntlet with Str 5, or whatever it is. It in no way grants Str 5 to the gauntlet. I don't know where you're even getting this from. Sure, you can use a ReTe guideline to hold as much stuff as you want, at which point the spell is affecting the stuff. Heck, a spell cast at touch (similar to Treading the Ashen Path) that lets you pick up any boulder you touch all day long works for me. (Throwing it is tougher though!)
It's a pity that despite trying very hard, I failed to convey in the spell description that the gauntlet makes every movement as if moved by a wearer with Strength +5 -- except that the force for those movements is not exerted internally by the wearer, but by the magic. A few people got it, but for such a simple concept I certainly did a bad job explaining it.