What's a good counter for Immortal Iron Dwarves?
I think it's important to realise that it's not just your group: a lot of people have been grumbling about the Immortal Iron Dwarves combination.  I've seen plenty of suggestions that it should just straight up be banned.  You're not "missing something" about how to deal with it - it's just very, very good, definitely to the point of being too good.

Having said that, if like me you prefer to play games as printed, even if that means occasional sessions where the odds are seriously unbalanced... presumably a player will have to pay top dollar to grab the combo if it turns up, since everyone knows how good it is.  All the other players will (or should) team up to impede the Immortal Iron Dwarves' progress.  Keeping them out of Mines so that the Silver Hammers don't rapidly accumulate seems like a top priority, and I think "he could take any region he wanted no matter what the defence" is a little bit of exaggeration: stacking piles of defenders up on the Dwarves' borders is going to slow them down, at least before they've been able to secure their full complement of Silver Hammers.

Yes, it's tough when a player has a combo that's just streets ahead of everybody else's, and  what should have been a fun, balanced 4-player game turns into a three-against-one.  But this is a known hazard of playing Small World, and the options are really limited to either banning known broken combos as a house rule; or accepting that every so often an annoyingly unbalanced game scenario will arise.  But even so, think of the glory if the other three of you manage to destroy the Iron Dwarf tyrant against overwhelming odds!  It'll be the best story since some puny hobbits managed to make it to Mount Doom and take down Sauron!