Is man responsible for the sins of his wife because he is the leader of the home?
The answer to your question is both “No” and “Yes.” That I actually force my wife to sin—as if I were making her do normal every day choices— I think is wrong. I cannot make her do something against her will (that is, without the use of the threat of physical force or the force itself). Therefore, in that sense, I am not responsible for her sin.
However, on the other hand, by creating an environment that causes her to stumble or that does not seek her best spiritual welfare I am sinning and responsible to the degree that I bring harm on her. We must seek to build up and nourish our wives in the faith, not tear them down.