They are simply argueing over who is higher on the totem pole than the other. That's it--it has nothing to do with liking or disliking each other. Both sound like strong minded mares and it sounds like the young one has recently come along to challenge the older ones turf.
Only two real options--
1. Pull their shoes--if they have them--trim the up and turn them loose together. They will settle it between themselves in short order--one of them will be squealing like a pig. You can stay close and "convince" the winner that enough is enough if you choose.
2. Keep them separated--that means not in turn outs with a common fence. That's like throwing gas on the fire-- "Oh Yeah!!"" "YEA!!"" etc etc.
I would vote for option 1. I've seen some cocky young fillies decide to tangle with my old lead mare and for sure she settles it quick. The next day all is well and they hang together eating grass and swatting flys.