But as the teacher you should be the role of discipline in that child's life, not hitting them, but you are also the first line of authority that child meets in life.

A parents discipline is muddled and blurred with the love they have; that should be the case, they are your family.
As a teacher, you should have a caring stance but ultimately a professional outlook on all the children. You are the first time the child is learning that not everyone in life will 'love' them like their parents, and that there are certain boundaries of conduct to be adhered to in the outside world.

It could in fact be weakening the bond with their family at a forumlative stage in life, because every adult in their world hugs them and seems to love them unconditionally; to them, how is there a difference?

A child's emotional development is vital, but that evolution in emotions is a parental influence; in the classroom you are the guiding light of education, and enlightening the child's knowledge.
The reward for the child from you is that they grasp key mental concepts and life skills. The reward should not be a 'hug'.