The revised Artificer in Unearthed Arcana gets extra attack from its Arcane Armament feature (pg 5):

Arcane Armament: Starting at 5th level, you can attack twice, rather than once, whenever you take the Attack action on your turn, but one of the attacks must be made with a magic weapon, the magic of which you use to propel the attack.

The Artillerist sub class allows the Artificer to apply a cantrip to a wand through Wand Prototype (pg 8):

Wand Prototype: By 6th level, you now regularly experiment with channeling different types of magic through wands. Whenever you finish a long rest and your woodcarver’s tools are with you, you can touch a nonmagical, wooden wand and turn it into a magic item. When you do so, you invest it with one artificer cantrip of your choice—even one you don’t know—that has a casting time of 1 action. As an action, you can cause the magic wand to produce the cantrip, using your spellcasting ability modifier (other creatures are unable to use the wand’s magic). The wand loses this magic when you finish your next long rest.

Any damage roll you make for a cantrip in the wand gains a bonus equal to your Intelligence modifier (minimum of +1).

When you reach 14th level in this class, you can invest the wand with two cantrips at the end of a long rest.

How does Arcane Armament interact with the Artillerist Artificer's Wand Prototype feat? Can you attack twice with the wand cantrip?

You cannot use the wand more than once per turn with these two features

Using a wand is a special action defined by the wand's description. The prototype wand says:

As an action, you can cause the magic wand to produce the cantrip [...]

You cannot produce a cantrip from a wand with the Attack action.

When you take the Attack action, Arcane Armament allows you to attack two times in that one action. Attack meaning to attempt to hit something with a weapon. But you cannot replace an attack with another action. And using the wand to produce a cantrip is not considered, in and of itself, to be an attack. Cantrips may have attacks as part of their effects, but producing a cantrip is not itself an attack.

When you produce a cantrip from the wand you have to use your full action to do so, which means normally giving up the option to Attack.

So, you cannot take an attack given to you by the Attack action and use it to use the wand to produce a cantrip.