Believe it or not, changing a Family Assignment in ChurchTrac is more common than you may think. Some situations in which Family Assignments are changed include a new marriage, adoption, divorce, children moving out, and remarriage.
To change a Family Assignment, click the "Edit" button for the individual you wish to change.
Once you're on the edit mode, click "Change Family Assignment".
You can then proceed in either adding the person to a different family or creating a new family for the individual.