If I play Back Off and stun an enemy unit at a battlefield, can I move Vex Mocking from another battlefield and Vex Apathetic from base to the battlefield with the stunned unit in the same movement?

To answer your question: No, you cannot move both Vex, Mocking and Vex, Apathetic to the battlefield simultaneously.

Here is the breakdown of why this is the case based on the game rules:

1. Triggered Abilities and the Chain

According to Rule 376 (Triggered Abilities), when you play Back Off and stun an enemy unit, the ability on Vex, Mocking ("When you [Stun] an enemy unit at a battlefield, you may move me to that battlefield") triggers and is placed on the chain.

Vex, Apathetic, however, does not have a triggered ability that allows it to move when an enemy unit is stunned. Its ability ("When an opponent plays a unit while I'm at a battlefield, [Stun] it...") is a reaction to playing a unit, not a movement effect. Therefore, Vex, Apathetic cannot move via this interaction at all.

2. Sequential Movement for Vex, Mocking

Even if you had multiple copies of Vex, Mocking, they would not move simultaneously. As established in RiftJudge FAQ #9455:

• Each triggered ability is placed on the chain individually.
• They resolve one by one in LIFO (Last-In, First-Out) order.
• They arrive at the battlefield sequentially, not as a single, simultaneous game action.

3. Vex, Apathetic's Movement

Because Vex, Apathetic lacks a "move" ability, it must rely on other methods (such as the Standard Move action during your Main Phase, provided it is not currently in a closed state or a showdown/combat). It cannot be moved by the triggered effect of Back Off or Vex, Mocking.

Summary: You can move your copy of Vex, Mocking to the battlefield because of its triggered ability, but Vex, Apathetic will not move, and even if you had multiple copies of Vex, Mocking, they would move to the battlefield one by one as their respective triggers resolved from the chain.