Since the idea of a "weapon-controlling" wizard that's not bound to undead sounds interesting, here some advice on how to perhaps improve this homebrew:

Generally speaking, you should always add, at what level a specific subclass feature is gained. Additionally, you have to be more specific, with what the abilities do. Right now the skills mostly state, that you get to animate objects and make them stronger. It's missing crucial information about how often each level's subclass feature can be used (per short/long rest) as well as what precisely things like "pummel and protect you from harm" or "become more damaging and deadly" actually do in terms of game rules.

2nd Level) Animation Basics: Since Mending is already a Wizard cantrip, I would add an additional feature to it (similar to how Mage Hand can do more things for the Arcane Trickster). Further, since this subclass is all about armor and weapons, it probably makes sense to have the wizard gain proficiency with simple and medium armor as well as with all simple weapons (and perhaps longswords).

2nd Level) Animate Sword: The way I understand this is, that you use a ritual to animate a longsword through your magic. I would change this to an action and extend it to non-magical simple melee weapons and longswords, since otherwise the ability can't be used if no longsword is around. I would have the weapon count as a weapon the wizard can attack with without needing to hold it in a hand. If the wizard wants to use two-handed attack variant, they still have to use one hand. I would limit this feature to 10 minutes, only allow the wizard to attack with it, have it be an action, and allow the wizard to use this feature as many times as Proficiency Bonus or Intelligence Modifier per long rest. The enchanted weapon can't be wielded by another creature or moved by a force exerted by less than (e.g.) 2000 pounds of weight.

6th Level) Animated Armor: Perhaps allow the Wizard to enchant a suit of armor to gain +1 AC and if the Wizard would be reduced to 0 HP, the armor "protect you from harm" allowing the wizard to drop to 1 HP, doff the armor in the process and the armor loses the enchantment. I would limit this feature to once per long rest. The Anchantment should be an action, could take 1 minute, and lasts until after completing a long rest or until it protects the Wizard from lethal damage.

10th Level) Animation Advanced: You could allow the wizard to not attack with the animated simple melee weapon/longsword from Animate Sword as a bonus action move the enchanted weapon up to 20 feet away as part of the same bonus action. If the weapon is further than a certain distance away (like 60 feet) it should no longer be controllable by the wizard but keep this enchantment.

14th Level) Animation Mastery: Perhaps allow the Wizard to now have two weapons enchanted. They could gain proficiency with martial melee weapons as well, would no longer require one of their own hands to make 2-handed weapon attacks, could also enchant martial melee weapons and also could enchant all magical melee weapons. The bonus action would still only allow them to attack with one of their two enchanted weapons but that way they can have two weapons be positioned on different sides and can use the right weapon for the job.

Not sure if this is strong, I assume it's not OP, and it would actually give meaning to your abilities.