I would like to know what state has jurisdiction over child custody modification case? The state that parent filing for modification lives where divorce was ordered in 2004, or the state that other parent and children have lived for almost 3 years.

It is s.c HOME STATE.and depends on jurisdiction.
There is lack of information in your post.

I agree with GV70.. the state where the order originated retains jurisdiction in all matters unless they give it away to another state. Federal unifomity law.

Yeah the location where the case was handled retains jurisdiction but you can ask the courts for jurisdiction to be moved to another location been through that also, have to get an attorney to do it or it is almost impossible or will take forever.