Page 27 of the 2e rules states:
- Any region entered by a moving Army must be either a free region (see Free Regions, on page 10) or an enemy-controlled Settlement that is free of enemy Army units. These are known as “regions that are free for the purpose of Army movement”.
— If a region is occupied by enemy units, it cannot be entered but must be attacked (see page 28).
So in your case Dale is free for the purpose of Army movement and though not at war, my read is that the North may still cross its own border back into Dale.
Just make sure you activated the North and advanced the North twice on the Political Track: once for the attack on Dale and a second time when the Easterlings troops entered Dale and captured it.