Unfortunately you are seeing the effects of a program called the "Interstate Driver's License Compact." (IDLC)
This is a contract between most of the states that lets them share driver's license information with each other.
So when you got the DUI in NC in 2007, the Secretary of State in NC put your DUI on the website of the IDLC, which allowed all the other states to see it. When you went into the DMV in California last June they looked up your record on the IDLC and saw the DUI. So at that point California started to make you go through their own process for DUI's. Thus, the new treatment and fees CA is demanding that you pay.
This is quite common these days. I handle many DUI's each year, and out-of state DUI's cause many problems for my clients. The only solution is to do what CA wants you to do.
Driving a car is considered a "priviledge", not a "right". So the state can take away your driver's license anytime they want, and it is very difficult to sue the state to get it back.
This is not considered "double Jeopardy" because this is not a criminal
case, it is a civil matter dealing with the secretary of state, not the criminal courts
Your only real chance of getting your license back is to do what California wants you to do. I realize that this seems incredibly unfair, and I agree. However, I do not make the laws, I can only tell you how to work with the laws to get your desired result.
I wish you the best of luck in getting your driver's license back!