Well, it depends on what the problem is. The rule of thumb is that the court is open to hearing a child's opinion on their living situation when they are 14 years or older. However, even with these children, the court does not just grant their desires. The court understands that teenagers are emotionally vulnerable and attempts to understand the motivation behind their desires. If they don't want to live with one parent simply because they are too strict, the court might not care as much as compared to if the child expresses that the parent doesn't take care of them adequately.
Even for children younger than 14, the court might care about what they want, but the courts typically want to make parents aware that visitation is not an option. Some parents come to court and say their young child did not want to go to the other parent's house, so they didn't force them to. Well, unfortunately, you have to lay down some parental discipline and force your children to go. Obviously, don't drag them kicking and screaming, but simply caving to your children's desires is not fulfilling the visitation arrangement and teaches your children that time with the other parent is not important.
So, in general, the court does care what your child thinks about visitation arrangements, but only if they are old enough, and only if they have a legitimate reason. In addition, you should make sure your children understand that visitation arrangements are mandatory, not negotiable.