12 weeks is a long time, If they were too busy to repair the car, then they should have offered a replacement or suggested you go else where. My take on it though, is that there were parts issues, and they cannot be responsible for that.
Adjusting the bill amount was pretty cheeky, If I were you, I would pay up before this gets any deeper and salvage the relationship with your dealer.
If you still think you were hard done by, you have the upper hand by paying the bill in full and then seeking a balance refund by going through the proper channels.