The way you can find the element id of the family is by filtering for families and then finding the desired family by name or some other characteristic:
void DeleteFamilyTest() {
Family famToDelete = null;
FilteredElementCollector fec = new FilteredElementCollector(uidoc.Document);
fec.OfClass(typeof(Family));
foreach (Element e in fec.ToElements()) {
Family f = e as Family;
if (null != f && f.Name.Equals("SomeFamilyName")) {
famToDelete = f;
}
}
if (null != famToDelete) {
uidoc.Document.Delete(famToDelete.Id);
}
}
Hope this helps!