I know with so many other things to work on this seems like kind of nitpicking, but warhammers really seem kind of out there in terms of balance.
There's a couple of weird things going on here. In terms of damage they are twice as effective as any other weapon available at the same time. They cost two metal while the mace (a solidly inferior option) costs four. They're also one handed, but the Lord Mace (which is only marginally more powerful) takes two hands. They are cheaper than broadswords and much more effective, even taking the combat speed modifiers into account.
A soldier with only a warhammer can attack twice for 24. A soldier with a broadsword can attack three times for 10. Not only is the warhammer going to be more damaging, the damage is much more frontloaded, allowing them to avoid a lot of retaliation strikes by simply killing the target on the first hit. If you put armor on your soldiers, the warhammer can still attack twice while the broadsword loses its extra attack. If you use a Great Warriors faction, the ratio tips even further in favor of the warhammer, because each weapon gets an extra swing and the warhammer packs a lot more punch.
There's a few ways to fix this. I'd start by switching the metal cost of the mace and warhammer, so the warhammer takes four instead of two. Then, I'd make the warhammer a two handed weapon. Shields could use a boost in their defensive bonuses, which would act as a buff for one handed weapons and bring them a little closer to warhammers.
Some of the other suggested changes, like simultaneous counterattacks, could affect the balance or allow the weapon to be balanced through other means, such as a defense penalty for the warhammer and a bonus for the broadsword. Another thing that could help balance things would be to only allow units to counterattack once per round. The swords get more attacks and suffer more retalations, especially considering that they're far less likely to kill an enemy outright so the extra attacks aren't really much of an advantage.
