Ok, so looking at the class a few times, I have the following thoughts:
1) Magical Tinkering does not belong. It seems to be a ribbon ability, but it is basically a reskinned Prestidigitation that lasts longer. This wouldn't necessarily be a problem, but the ability is weighted heavily enough to be the only other ability provided in addition to spellcasting. This is supposed to put it on par with a Wizard's Arcane Recovery or a Sorcerer's access to their archetype at first level, since these are the other two classes that get access to Spell Casting at level 1. Erase this ability and give the Artificer access to their first archetype ability at level 1.
2) Flavorwise, neither the alchemist's nor the arterialist's mechanical abilities seem thematically linked to the concept they are meant to represent.
3) Take out the pets for both archetypes. This gives each archetype more design space for thematically appropriate abilities, and provides an opportunity for a new archetype focused on making and using constructs.
4) The original 3.5 version of the Artificer had a means to replicate spells from any other spell list. I'm not sure how they would do it on the existing framework (I've figured it out for my own homebrew version), but they need an ability similar to a Bard's Magical Secrets.
5) The Right Cantrip for the Job is a genuinely good ability, fits the Artificer concept, and I'm glad it's included. However, it needs to come online well before level 10.
6) Not sure the Artificer needs Tool Expertise. Proficiency in their tools is enough. Tool use seldom comes up in the games I've played except Thieves' Tools. I would prefer this was scrapped to allow design space for less mundane abilities more related to their archetype or the creation of magical items. Artificers are skilled in creating things, but I would not say they are Artisans. At least to me, they are more about the binding and manipulation of magical energies to replicate spells and magical enchantments.
7) Spell-Storing Item is interesting. I need to reflect on this ability a bit more, but I am leaning towards liking it. It is effective at replicating a wand, and has a good amount of power. It is also similar to a Wizard's Signature Spell ability, but can be used by other characters.
8) Infusions are interesting. I don't exactly like the way it is executed, but it does allow for the feel of creating magic items.
9) Arcane Weapon seems too powerful in comparison to similar spells. It's certainly more powerful than Divine Favor (another 1st level spell). This seems to be at least a 2nd level spell, on par with Magic Weapon. You do more damage, but don't get the benefit of bonus on attack. Additionally, placing it at level 1 makes it a ripe choice for Magic Initiate.