Hi,
If you caused war among races, they actually are really fighting. Now it depends if they are at the same time in war with others, if so than the "new war" will not become a more important priority to them...Even worse, the new war will maybe slow down the AIs ability of concentration..
Sometimes you can see fleets fly by each other without attacking, because it seems they are following an order, which might not change so quickly (same like in the army on earth: orders are orders...
)
There is no possibility to force one race to focus more on another. Besides, this could be a funny new "diplomatics" option, for example asking: "Dregins, I give you 500bcs but ask you to please kick Altarians' asses a little harder"
The good point is that during the time they are fighting, you can lay back and recover a little...