If a parent is awarded sole custody, this, in turn, gives them absolute autonomy in the decision-making process (and the execution of those decisions). This is because a parent with sole custody has both legal custody and physical custody of the child/children. The legal custody aspect is what gives the parent the ability to make all of the impactful choices regarding your child, while they are still a minor, without needing to consult the other parent for their input. There is a multitude of reasons why only a single parent is given the ability to make these life decisions for the child, and some of them do revolve around the non-custodial parent’s decision-making abilities and history.
These same reasons could be utilized and highlighted by the custodial parent in their effort to deny visitation. For example, if the other parent has a history of alcohol abuse, and upon arriving to pick up the child for their visitation day, they appear intoxicated; the custodial parent would have a good reason not to let the child go with this parent. In such a scenario, it would be wise to document this, most efficiently through video, as the other parent may mention it in court in order to make a case that you are violating the visitation agreement.
It is a wide-held belief by the courts that a child develops best when in regular contact with both parents, and so even with sole custody, it is rare that a parent and child never see each other. So, if you are planning on requesting to deny your the other parent visitation entirely, it will require very thorough documentation (as credible evidence), and a significant pattern. An isolated incident will probably not suffice, but repeated instances could.