If I play Relentless Pursuit on a unit that is readied, does the unit exhaust from moving? Same thing with Emperors Divide?

No, neither Relentless Pursuit nor Emperor's Divide will cause your unit(s) to exhaust when they are moved.

According to RiftJudge FAQ #9814 and RiftJudge FAQ #8882, when a unit is moved by a card effect, its state (Ready or Exhausted) does not change unless the card explicitly states otherwise. Since neither of these cards includes an instruction to exhaust the units being moved, they remain in their current state.

Key Points:

• Effect vs. Action: This is distinct from a "Standard Move" (Rule 144), which is an inherent action that does require exhausting the unit as a cost. Because Relentless Pursuit and Emperor's Divide move the units via a card effect, they bypass the exhaust cost entirely.
• Consistency: As confirmed by RiftJudge FAQ #6925, when a card effect explicitly says to "move" a unit, a readied unit stays readied unless the card specifies it should become exhausted.
• Readied Status: If you use Relentless Pursuit to move a readied unit, it will arrive at its destination still ready. Similarly, if you use Emperor's Divide to move readied units from a battlefield to your base, they will remain ready upon arrival (RiftJudge FAQ #8919).