Is there any point in buying another hat to ensure I get invited to the ball? I mean if you buy two hast is the effect twice as good. I keep getting offered the same items (after i have them) over and over again.

You get invitations earlier.

If you are hostile with the spanish and sneaked into town to visit the gov you will get an invitation to the ball. As lang as you have any spanish title. So be sure to get one early in the game.

The second hat you're being offered is better. Each special item has an improved version of it, which you can only buy after gettin the first. For example, you buy the balanced sword, then you can get teh perfectly balanced rapier, which is a better version of the balanced sword.