Your kids hate their new step-parent can you legally reduce the other parent's visitation time?

The encouraging thing about the custody statutes across the U.S. is that they recognize that not only parents have right to visit their children, but children also have the right to visit (or not to visit) with their parents depending on the circumstances. All matters pertaining to children are viewed from the lens of “the best interest of the child.”
If a relationship such as a step-parent relationship is causing enough disruption in a child’s life, and this step parent resides with the noncustodial parent, the custodial parent can definitely go back to court and make a motion to either stop the visitation from happening around that step-parent, or if the visitation continues to have it supervised, or to reduce the visitation time. So, whereas the child has been ordered to overnight visits with a noncustodial parent and a step-parent (who, it can be demonstrated, is not in the child’s best interest), that visitation can be reduced to just an afternoon or two per week, or even to visitation at another location other than the home of the step-parent.
After a certain age, children can also, through their court appointed lawyers, express their wishes to the judge about where they want to reside and whether they want to visit with the non-custodial parent and whether they want to have a relationship with the step-parent. Depending on the circumstances of the particular case, the courts would make a determination about how the visits will be achieved. Many questions will be asked and answered to get to the bottom of what is really going on, however.
Depending on the answers an investigation yields, maybe the actual parent (not the step-parent) will have to visit with the children in a location other than at the home where the step-parent is present. Maybe there will simply be less visitation time, such as reduced overnights, reduced summer vacations, etc. In extreme situations where the step-parent relationship with the child is sufficiently bothersome, at the child’s request, all visitation may be terminated as well. But that is the extreme and unusual case. Mostly, there will be some kind of supervised visitation so that a court appointed person can ascertain what is going on when the child is visiting. The recommendations of a psychologist will also taken into account and the child’s preferences will factor heavily, especially if the child is over 12 years old.
The custodial parent will likely also be investigated to see whether there is “parental alienation” going on. A custodial parent can alienate the affections of the child for a step parent just as easily as they can alienate the child from a biological parent. A step parent does not have the right to visit with the child but is in fact a legal stranger to the child. So the concept of parental alienation is a bit of a stretch. But not totally irrelevant. Again, the circumstances of the situation will determine how much visitation the court will allow, if  it is determined that the relationship the child has with the step-parent is not in the child’s best interest.
Where the step-parent resides with the custodial parent (as opposed to the noncustodial parent), one remedy could be that the custodial arrangement changes and the child will be placed with the other parent, or even a foster parent.
There are myriad outcomes that depend on the facts of each case.