Please don't punish her for having learned things that you haven't been able to... that isn't her fault! Nor is it fair to punish her for the fact that your dad is in control of everything.

Talk to your dad. Ask him to help you gain some more independence in regards to your finances. Tell your fiancee your anxiety over the accounts, and see if she would sit with you and your dad to take part in the conversation so that she could help address your dad's concerns and he could ask her questions too. Why not ask your fiancee if she would be up for being a joint-person on your account? If she's alright with that, then bring that to your dad and explain that as you're getting married you and your fiancee think that you should be in control of your own finances. Then go to the bank with your dad and your fiancee and get things changed over.