If Tideturner is stunned by Vex does the other unit targeted in its trigger still move?

Yes, the other unit targeted by Tideturner will still move, even if Tideturner itself is stunned.

According to RiftJudge FAQ #10318, when Tideturner's play trigger resolves, the swap is handled as a single effect. If Tideturner is stunned (which also applies a "cannot move" restriction), Tideturner itself will fail to move; however, the other targeted unit will still successfully move to Tideturner's original location.

This occurs because the instruction to move the targeted unit and the instruction to move Tideturner are separate parts of the same ability. Per Rule 359.3.e.11, instructions that can be partially followed are followed as much as possible and ignored otherwise. Since the stun/movement restriction only applies to Tideturner, it does not prevent the other unit from completing its part of the swap.

Note: This interpretation relies on the partial resolution of instructions as detailed in Rule 359.3.e.11 and the FAQ entry #10318 regarding Tideturner's interaction with Vex, Apathetic.