I wanted to know what happens when two co-workers are not working well together. What are all the steps to make sure that all workers get along for the children. If the matter is not resolved who will the staff member go to next if the two co-workers can't resolve this matter.

Are these two staff members in the same classroom? Often the supervisor will sit in on a classroom to get a read on the situation. At our centre we have a staff liaison (member of the board) that the staff members can speak to if they feel they can not discuss the matter with the supervisor.
I like to promote team building exercises during staff meetings to keep the team working well together. We also actively search for professional development in team building.
If the supervisor has an open door policy, staff will feel comfortable enough to come in and discuss the situation before it gets out of hand.