I just don't understand how she can dictate orthodontics when it is specifically in the decree that i make the decision. It's not a huge amount of money and i am also paying the same extra expense.
She cannot "dictate" orthodontics. She cannot "dictate" anything. You have the decision making rights. However, if you make a decision that costs her an unnecessary amount of money, she does have the right to protest that.
Now, it turns out that the financial difference is not as bad as you originally stated it was going to be, but there is still an appreciable difference. Therefore the possibility exists that you will only be able to require her to pay 1/2 of what the less expensive option would have been.
The possibility also exists that you can demonstrate that your decision was reasonable and therefore she would have to pay 1/2 of the actual cost.
Keep that in mind going forward dad.