Many guys here misinterpret the Captain/First-Officer model for marital leadership as a formal military/Star-Trek-style, appointed or agreed-upon official chain of command. This is a flawed interpretation which will serve you poorly; the informal "Leader-of-the-Pack"/"Best-Mate" leadership model, which is natural to small voluntary human social groups, should be your goal.
Forget Star Trek, the Army, and adult supervision
The military/Star-Trek-style, formal chain-of-command view of leadership is actually deeply blue-pill, because the leader is appointed by some higher external authority (admiral; Star Fleet headquarters; teacher; Bible), or elected or negotiated (which means that it can be withdrawn or renegotiated), and often ends up with a beta or inferior man in charge. (Have you ever wondered why so many red-blooded ex-military/police show up here with deeply blue-pill ideas and behavior and failing marriages? Now you know why!)
Formal, chain-of-command leadership is unnatural, inefficient, demotivating, and an ongoing source of conflict and resentment in small, voluntary or informal social groups (such as families; small gangs; groups of friends; pickup sports teams). In such groups, the leader emerges organically, based on his superior "alpha" and social traits. The leader is never formally voted on or declared, but everybody in the group knows who the true leader is and defers to him, his vision, plans, decisions, and judgments. This is informal "Leader of the Pack" or "pirate captain" leadership, with voluntary followers inspired by the implicit "captain" and his vision. If well led, small groups of inspired and motivated followers are generally much more productive, harmonious, cohesive, and happier than formally structured organizations.
In such groups, a "right-hand man" or "best mate" often emerges with whom the leader preferentially takes counsel, delegates secondary leadership, and entrusts to represent him or lead when he's away. The "best mate" earns this trust and role by being the most loyal, dedicated, diligent, and capable follower fully committed to the leader's vision and mission. This is the informal "first officer" role that you want your wife to spontaneously and willingly take up.
Becoming the Leader of your Pack
Leadership of the pack is never negotiated or discussed, but is simply claimed by the actions and behavior (not words; don't do this) of the "alpha". If you have to negotiate being the captain, you aren't a real captain.
Think about it, if she has to approve it, it means she is still leading. Leading is not achieved with verbal arguments so she recognizes your leadership.
This excellent post by /u/strategos_autokrator describes how to become the leader of your pack:
Leaders don’t need permission to lead. They just lead, period. Those that like your vision follow willingly. Those that don’t, well, they are useless to your vision, so you won't miss them when they stay behind. It is that laser-beam focus of the vision of the leader and doing whatever it takes to get to the goal that inspires others to follow. Thinking others have to follow so you can lead is having it all backwards, and this backward thinking is why she doesn’t trust you to lead.
Don't negotiate or discuss "who's the captain" with your wife; just be the superior productive, effective and charismatic leader of your pack, and she will likely follow and happily assume the "first/best mate" role over time.
For you hopeless Star Trek nerds, Khan, not Picard, is your model.