A child in the United States is able to testify in court at the age of 13 (or there about) and can choose not to see a parent. This will be taken into account when the judge makes a decision but children over the age of 13 are listened to in court and their thoughts are taken as a high consideration. This means that if a child wants to refuse visitation this will usually happen.
If the child is under the age of 13 they can consult their social worker or parenting coordinator who will take this into account and take the thoughts and feelings of the child into the court with them and explain this to the judge. This does not hold as well as when the child is over the age of 13 and may not be taken into account.
In the UK, children can make their thoughts known when a contact order is made and their thoughts and feelings are taken into account when the judge makes the decision. They may make an order along the lines of ‘child may have contact with their parent’ which gives the child the choice to make the contact with that parent rather than the parent being allowed to visit and contact their child. These contact orders in the UK are used up until a child is 16.
In all cases, it is the judges responsibility to ensure that they make a ruling that is in the best interest of the child/children involved.