What warrants supervised visitations, and who is responsible to transport the children to the agreed upon visitation location?

Whether supervised visits are ordered is very fact-specific in custody cases, depending on factors such as the allegations giving rise to the requesting relief, the age of the child, and any past domestic violence.  Who supervises is also fact-specific; the court has to make a determination as to whether the proposed supervisors will ensure the child(ren)'s safety, even if it is their own family member who they are supervising.  Sometimes family members are appropriate supervisors; other times, it benefits both sides to have a neutral supervisor, such as a court-approved agency, if available.  However, there is a cost involved for these types of supervisors, and the court will need to determine how those costs should be shared.