If I have Traveling Merchant and Yasuo Remorseful Attack on the battlefield where my opponent has control, can I choose either Traveling Merchant or Yasuo to resolve first?

No, you cannot choose to resolve Traveling Merchant and Yasuo, Remorseful in either order. Their abilities trigger at different times and in different game states.

According to RiftJudge FAQ #4077, move triggers (such as Traveling Merchant) are distinct from the combat sequence and must resolve before a Showdown begins.

The Sequence of Events:

1. Movement & Move Trigger: You move Traveling Merchant and Yasuo, Remorseful to the battlefield. This move initiates a chain for the Traveling Merchant trigger.
   • Traveling Merchant's "When I move" ability is placed on the chain.
   • This chain must resolve completely before the Showdown begins.
2. Showdown Begins: Only after the Traveling Merchant chain has fully resolved does the Showdown begin.
3. Initial Chain (Showdown): Now that the Showdown has begun, the Yasuo, Remorseful "When I attack" trigger is placed on the chain.
   • Because Yasuo is attacking, his ability triggers as he gains the Attacker designation upon the start of the combat (Rule 383.4.e).
   • This is an Initial Chain for the Showdown. As established in RiftJudge FAQ #8871, only Reaction speed cards may be played during this initial chain.

Key Rulings:

• Move Triggers Resolve First: Per RiftJudge FAQ #4077, the move trigger resolves before the Showdown starts. The "When I attack" trigger cannot be placed on the chain until the Showdown has officially commenced.
• No Choice in Ordering: Because the Traveling Merchant trigger must be resolved entirely to clear the chain before the Showdown (and thus the Yasuo trigger) can even exist, you never have a situation where both are on the chain simultaneously to choose an order.

In summary, Traveling Merchant resolves, then the Showdown begins, and then the Yasuo, Remorseful trigger is added to the Initial Chain.

Note: I could not fully verify the specific mechanical details of the Traveling Merchant trigger against the retrieved rules.