Usually there's nothing to preclude a custodial (or non-custodial) parent from allowing contact with their new "boyfriend" or "girlfriend" during authorized parenting or visitation time.
There may be legitimate issues about safety if there is something unwholesome about the particular person and contact with your child, such as a history of violence, criminality, substance abuse, child abuse or neglect or even cigarette smoking, but just the fact that the new girlfriend/boyfriend or their family is around your child is not a ground for objection.
Certain limited objections, such as the child calling the new boyfriend/girlfriend/stepparent "dad or mom" or "disparagement" of the biological parent can be worked into a family court order, but a sweeping ban of the sort you are seeking where the parent can't consort with someone of the opposite sex won't be entertained by a family court, whether you appeared pro se or with an attorney. There's no vow of celibacy that's imposed by a family court.
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Unless there is an issue of what is going on in the bed or some other serious consideration, the boyfriend is essentially entering the familial structure at the mother's house and that is not unusual. Consider that fact that he may someday be her husband.
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