Does Vex Apathetic at a Battlefield mean that a Sprite unit from Sprite Mother will not be able to move?

Yes, if your opponent has Vex, Apathetic at a battlefield, a Sprite unit created by Sprite Mother will be unable to move that turn.

Here is the breakdown of why this happens:

1. Trigger Condition: Vex, Apathetic’s ability triggers "When an opponent plays a unit." According to RiftJudge FAQ #9240, this ability triggers regardless of where the unit is played on the board, provided Vex is at a battlefield.
2. Effect: When the Sprite enters the board (via Sprite Mother), Vex's ability triggers. It [Stun]s the Sprite and applies the restriction: "They can't move it this turn."
3. Movement Restriction: Because the Sprite is stunned and restricted by Vex's ability, it cannot be moved for the remainder of the turn.

As noted in RiftJudge FAQ #9475, this interaction is definitive: Vex's ability resolves, stunning the unit and preventing its movement for the turn. You cannot use other spells (like Ride the Wind) to move the unit in response to Vex's trigger because the chain is active (Closed State) once the unit is played.