Can a father keep a child from the mother on designated visitations?

If it is court ordered and she is refusing, she is in contempt of court.

I'm not sure I totally understand your question - but yes, a father can keep the child in his possession to the exclusion of the mother during his allocated parenting time. This would not be considered parenting time if the father could only see his child with the mother's supervision, it would be supervised parenting time.