Are overnight visits restrictef when one parent has married a registered sex offender and the other parent does not agree

If there is no language in the father's curernt child custody orders that speaks directly to the issue, then the mother isn't prohibited by that order from having the children overnight, though the registered sex offender, if he was prosecuted and convicted of a child sex crime, may be violating a condition of his sentencing orders.  To address this, the father needs to file a petition to modify the child custody orders.  However, he'd be well advised to obtain as much information about the offender as possible, such as the particular circumstances of the crime, when it occurred, and what, if any, sentencing conditions he's under regarding his contact with children.   This is definitely a case in which I'd recommend that the father consult with an experienced family law attorney, and the sooner the better, if the mother is demanding overnight visits.  There are emergency orders that can be issued almost immediately that would prohibit the visits under the right circumstances, while the modification case is pending.