The child cannot opt out in most jurisdictions until they reach eighteen years of age. If the non-custodial parent has court ordered visitation and the child does not go for those visits, then the custodial parent can be held in contempt of court. If there is a legitimate reason why the child does not want to go, then you need to petition the court to change the visitation order. Be aware that courts do not like to deny a parent visitation with their children and will not do so without a VERY compelling reason.
When a child refuses to visit the other parent the primary custodial parent must first take steps to determine the cause of the refusal. A professional may be of help at this time. The child may have legitimate reasons and once identified both parents must work together to address the problem. The non-custodial parent may need some advice on how to spend quality time with the child so the child feels both welcome and comfortable in the non-custodial parent's new environment.
This is a common mistake made by non-custodial parents. The child misses them and looks forward to spending time with them but that time comes and there is a stranger present. The child's comfort level plunges. Being forced to spend visitations with people other than the parent is not a good idea until the child has had a chance to adjust to the new family dynamics between the child and the parents. The dynamics of coping with the father's new partner should come much later.
Uncomfortable sleeping arrangements can make a child reluctant to go for visits. If there are other children in the picture (belonging to the non-custodial parent's new partner) they should be allowed to develop a relationship gradually. A common problem arises for the child whose non-custodial parent makes no special notice of the child during visits and expects the child to spend their time with those other children as part of a new "family unit". In those situations the child has lost a special parent-child connection with the non-custodial parent. The option of spending some private quality time with their parent should always be an option.
If the child's concerns are serious and the non-custodial parent will not cooperate, the custodial parent may need to return to court for a modification of the visitation order. On the other hand, when the situation is evaluated by the court it may find that parent alienation is at the root of the difficulties and if serious, the custodial parent may well lose physical custody to the other parent. Alienating a child against the other parent causes irreparable and long lasting harm.