I understand why men lead prayer in public and not women (I Timothy 2:11-12; I Corinthians 14:34). But what about my wife and I praying together in private, is it wrong for her to lead us in prayer?
The passage in I Corinthians 14 deals with the worship service (I Corinthians 14:23) and thus does not apply in a private family setting. However, the passage in I Timothy contains general principles of Christian conduct. Thus, the command "Let a woman learn in silence with all submission. And I do not permit a woman to teach or to have authority over a man, but to be in silence" (I Timothy 2:11-12) still applies. "Silence" is not absolute silence, but the portrayal of a quiet attitude (see "Silent in the Churches" for more details). It doesn't forbid the asking of questions because even in the situation of worship where women are not to speak, they are encouraged to ask questions at home (I Corinthians 14:35).
The one saying a prayer is leading those who are listening. It is a position of authority. That position was given to men. "For Adam was formed first, then Eve. And Adam was not deceived, but the woman being deceived, fell into transgression" (I Timothy 2:13-14). It is not proper for a wife to take on a position not given to her by God, nor is it proper for a husband to place his wife in a position not authorized by God. "Imitate me, just as I also imitate Christ. Now I praise you, brethren, that you remember me in all things and keep the traditions just as I delivered them to you. But I want you to know that the head of every man is Christ, the head of woman is man, and the head of Christ is God" (I Corinthians 11:1-3). We do not have the right to change this ordering, even on a temporary basis.