The details of the warrant and charges do matter, of course, but I stand by my answer. The person seeking to get the warrant admitted must show relevance to the issues in the proceeding, and in a lot of cases that's going to be difficult to do.
I may have explained myself poorly. Let me give you an example of what I was talking about. Dad has a warrant (for anything, it doesn't matter what) and is driving around with the children during his parenting time and gets pulled over for something (doesn't matter what), the police see that there is a warrant for his arrest, and therefore arrest him in front of the children. In a best case scenario mom will be called to the scene to collect her children and therefore the trauma to the children will be the act of seeing their father arrested, and nothing more.
In a worst case scenario social services ends up collecting the children from the scene, and mom has to jump through all of their hoops to get the children back, (which could take weeks or even a month or two) and there is a much greater level of trauma to the children.
It is therefore conceivable that a family court judge, realizing the potential for such trauma to the children, would require that the parent clear up the warrant prior to having unsupervised visitation. The judge could conceivably want dad to have another adult or adult family member present during visitation to ensure that nobody had to be called to the scene to collect the children.