What if the husband is convinced of the head covering, but his wife isn't?
Since the head covering is a sign of submission, the answer is no different from a husband who is convinced that his wife should be submissive, but she isn't. The command: "Wives, submit to your own husbands, as to the Lord" (Ephesians 5:22) is to the wife, not to the husband. A wife must choose to follow this command; no one can make her do so. In the same way, the command to wear a covering during prayer is given to women in I Corinthians 11 and the command not to wear a covering during prayer is given to men. Each must choose to follow the command. Ultimately, God will decide who was faithful to His commands. "Who are you to judge another's servant? To his own master he stands or falls. Indeed, he will be made to stand, for God is able to make him stand" (Romans 14:4). Pray that your wife comes to understand the Scriptures, and pray that God grants her a home in heaven. Teach what you know about the subject when the opportunities arise and know that you are doing the best you can for the Lord.