[thejeff]

Provinces don't move.
Battles are resolved in either province number order or in reverse order, apparently randomly. Many things in dominions are done this way.

If you're talking about army movement, I'm not sure that's clear. It should only matter when 2 armies are trying to invade each others provinces or a third party's province.
In the latter case, the armies always move, so only the order the battles take place in is important. This again appears to be random, possibly by nation id (or reversed).
The first case is less well understood. I do not believe it's as simple as whichever nation/province/army/whatever moves first gets to have the fight in the others province. If it was, using a single commander to block invaders would work about half the time, which it doesn't seem to. I've also seen, rarely, armies swap places.