Is it wrong for a wife of a preacher (who is not a pastor and does not have his own church) to attend a different church, even though they both believe in the same faith (Jesus the Christ)? I don't believe it's dividing kingdoms because that means believing in two different faiths and that's not the case with us. What do you think?
First, churches belong to Christ, not to any person. "And I also say to you that you are Peter, and on this rock I will build My church, and the gates of Hades shall not prevail against it" (Matthew 16:18).
Second, elders, also known as bishops, overseers, or pastors, are different from a preacher, who is also known as an evangelist or minister. Some preachers do become elders, but all elders are not preachers. They are two separate jobs that have some overlap. See "Pastors and Preachers" for more details.
Third, whether you were a preacher's wife or just another member, the answer would not vary.
You did not say why you are choosing to attend a different church than your husband. While you claim to have the same faith as he, I can't help but notice that you only claim a vague faith in Jesus as your common belief. God doesn't look at it this way. There is only one faith and there is only one church (Ephesians 4:4-6). There are numerous corruptions of the true faith and true church, only one is acceptable to God and Jesus, and that is the church Jesus built for himself. The description of that church is found in the book Jesus left for his followers, which is the New Testament.
Thus, if you mean that you want to attend your denomination (which means "division" by the way) while your husband attends his, then it isn't going to make a huge amount of difference since the two denominations are both not following Christ in slightly different ways. It will make a difference to your children. Children brought up in an environment where mom and dad believe differently tend to grow up with no belief of their own.
If one of you is attending a church that is fully following the teachings of Christ and is not apart of any denomination, then I can see why the other wants his spouse to join the true church with him. Most people want their spouse to be with them in heaven after this life is over. So wouldn't it be better to sit down together with your Bibles open and study together what constitutes a true church of Christ and find one to attend together?