Hi Julie,
Reading between the lines, it looks like you're thinking of 'law' as something like 'a set of rules enforced by the state.' Then, you are of course right that 'law' would seem to be little more than a stage of development within a broader field of 'conflict resolution.'
I don't think that's the same definition of 'law' that I have, though. I would think of 'law' as even broader than 'conflict resolution,' in fact; something like interwoven sets of 'norms' (social norms, but also economic norms, behavioral norms, etc.) plus sets of enforcement mechanisms (or encouragement mechanisms; I'm trying not to get caught up in the language).
Moreover, even sticking with 'law' as 'enforced rules,' I'm not sure it's demonstrably lower than, say, mediation. Mediation is, as you identify, essentially a conflict-resolution mechanism that in some ways incorporates inclusion and care (though in other ways not, I would argue; depends on the mediation system in question, but it can tend to lack the discerning (stereotypically 'masculine') care in favor of ensuring that everybody is heard and feels justified, which can be better sometimes but definitely isn't always). A skilled mediator might indeed be able to integrally resolve conflicts, but I seriously doubt that mediation could, for example, handle violent criminals, or desgregate the south. I think an integral legal system would recognize that many situations call for telling one party they are required to do X no matter how much they don't want to, something mediation isn't designed to do.