I don't think it's worth it to betray the Beornings as Dale, personally - unless it looks like they are about to betray you. If you see them start to put armies on or near your territory, you might want to attack them preemptively to potentially avoid losing allies (since the AI factions tend to side with the attacking faction when forced to choose between allies).
The Beorning lands are rather profitable and probably easy for Dale to develop (they are either Homelands or Fiefdoms for you; can't remember). Oldford in particular can get some nice trade going. But it'll still take you time to build them up, and in the meantime you'll be at war with the Beornings, your faction leader will probably lose some Authority (making your generals/governors less loyal/efficient), and you'll lose out on the trade that you currently have with the region.
Also, the Beornings somewhat shield you from factions in the west and south. If Adunabar or Tharbad is doing really well across the Misty Mountains, they can only really attack you if they first take those 2 Orc forts: Gundabad and Northern Hold, I think. That makes it easy for you to defend the area. If you take out the Beornings, western enemies could also attack you across the High Pass, further south. And then, whoever owns the Brown Lands can just march up the Anduin and attack you as well.
But since you have military access with the Beornings, what you *could* do is send a stack through their lands and attack these other factions before they get close to you - projecting your power safely. Make it a real viking raid - plunder some settlements, destroy everything, and move on to the next. The target faction may want to ceasefire with you (since you don't border them), and you can usually get them to pay you a good deal of cash for such an agreement. Just a thought
I haven't tried such a strategy with Dale, but it seems to me that they would be really well suited for it, since you can afford to maintain a big raiding army, and said army can be of very high quality, with a good mix of terrifying troops.