My husband is not a Christian. If a woman is not to lead prayer at home when her husband is present, then how are my children to learn to thank God for their food? What are my options?
Where the prior answer assumed that both the husband and wife are Christians, you question deals with a man who has not yet submitted himself to his Lord. Paul states that there is a chain of authority, "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 11:3). When one link in that chain is not acting in accordance to the will of those above, then those below must still continue to follow the higher authority.
For example, all governments exist by the will of God. "Let every soul be subject to the governing authorities. For there is no authority except from God, and the authorities that exist are appointed by God. Therefore whoever resists the authority resists the ordinance of God, and those who resist will bring judgment on themselves" (Romans 13:1-2). As citizens of a government, we are required by God to give obedience to our government. But when that government steps out of its God given authority and orders its citizens to act against God's laws, God comes first. We see this when the highest court in Israel ordered the apostles to cease teaching about Jesus. "And they called them and commanded them not to speak at all nor teach in the name of Jesus. But Peter and John answered and said to them, "Whether it is right in the sight of God to listen to you more than to God, you judge. For we cannot but speak the things which we have seen and heard"" (Acts 4:18-20). When they were hauled into court a second time, "And when they had brought them, they set them before the council. And the high priest asked them, saying, "Did we not strictly command you not to teach in this name? And look, you have filled Jerusalem with your doctrine, and intend to bring this Man's blood on us!" But Peter and the other apostles answered and said: "We ought to obey God rather than men"" (Acts 5:27-29).
The same holds true in a family. The husband ought to be the one teaching his children the ways of God. "And you, fathers, do not provoke your children to wrath, but bring them up in the training and admonition of the Lord" (Ephesians 6:4). But since he is not yet a follower of Christ, and thus unable to do this, the teaching of the children cannot be discarded. A wife will have to do the best she can in less than ideal circumstances. In this case she is not usurping her husband's authority but filling in for a husband who hasn't yet stepped up to his duties.