I can't seem to find the right "kind" of monster/location to attack for the dwarven alliance quest.
I think I am just missing something obvious here, maybe its like with the centaurs whose quest calls for killing ogres, who are a giant subtype and found in places guarded by "giants" (alongside actual giants)
So, help please.

I explored about 6 and didn't find it.
Every time I chose to burn it to ground afterwards, does that matter or have I just been unlucky?

Thieves Guild (the one that gives you a choice to burn it or not after the battle) is a different type of location than Lair of Bandits. But it happens that you don't find the axe in a Lair of Bandits after conquering it (it's random, so if you don't find it, and then go back in time and fight the battle again, you still have a chance to find it).

You always can find Lair in province, which had robbers as neutral guards.

thank you.