Quick answer
Supervision and supervised exchanges are different arrangements; each needs workable, specific terms.
Do now
Explain the safety concern with evidence and identify appropriate services, availability, costs, and scheduling. Ask whether a temporary order is needed. Clarify who supervises, what conduct is permitted, and how concerns are reported.
Watch for
A relative informally watching a visit may not satisfy an order requiring an approved provider. Do not assume a service is available without confirming it.
Official sources
NJ Courts — Representing Yourself, NY Courts — Custody and Visitation, DC Courts — Family Court Self-Help Center, NJ Courts — Domestic Violence.