How to deal with strong PD?

[Sombre]

Go around them. Attack a different province.

If it's a real choke point then the best way to deal with it is to bring an overwhelming force - your main army. If this army isn't likely to be enough, well then you'll have to direct your research to some stuff that invalidates PD, like SCs, powerful battlemagic etc.

Most PDs are vulnerable to spells which affect masses of meatshieldy troops, like aoe damage, poison, morale reducing spells, stuff with awe and so on.