I was just reading over the rules again and I noticed something about toughness I think I have been playing wrong.

So if I defend with a character with toughness(1) that has 2 life and my opponent is attacking my kingdom with a total of 3 power. He only has to apply 2 of the power to my character before applying the other one to my kingdom. This is because toughness does not kick in when damage is being assigned.

Is this the way everyone has been playing?
 

Yes that is correct. Toughness is just something to protect units, it doesn't make them better at blocking damage to their capital.

Correct. Somepeople think of Toughness as an extra HP. It isn't, it is a form of damage cancel, meaning your opponent can sneak that extra point of damage to your capital and without another card effect, there is nothing you can do to prevent it.

"I am the Prince of Dorne. Men seek my favor."

I guess I was doing it wrong.  I thought you had to assign three damage to a 2 hp unit with toughness in order to kill it before you could assign capital damage.

Instead, according to this, all you have to do is assign as much damage as it has hp, and the rest can go to the capital, even though the toughness will keep it alive?

If you want to kill a toughness 1 unit with 2 hp, though, you would have to assign three damage, right?  As soon as you assigned three, toughness would cancel one, so you still have two to kill it.

Yea I was playing wrong at first, but know I read the rules again I see that the dwarfs are not as strong as once I thought.

Dwarves are ridiculous, if they arent as strong as you once thought, I quiver to hear how resiliant you thought thye were in the beginning.

Yes to kill a unit with toughness you must "over assign" damage equal to the toughness rating... and hope they have no tactic or card in play that will prevent cancel one of the damage. 

"I am the Prince of Dorne. Men seek my favor."