You need to talk to your attorney. The DMV is a deep hole with many different types of actions that can be taken. Were you on DUI probation when you got the 2nd DUI? On a 2nd the DMV will do suspension, but allow a restriction. You may be able to get a restricted license as soon as 90 days but it all depends. Best to talk to your attorney. If you did not get one... well try calling the DMV for an explanation.
Of course, every DUI case is different and you should consult an experienced DUI defense attorney in your area with questions regarding your specific case. It is always in your best interest to have a good DUI attorney represent you when you have been arrested for a DUI.
The DMV hearing, also known as admin per se, is a separate and parallel track to the criminal case. DMV makes its own independent decision to suspend your license after the hearing that you had with the DMV hearing officer. They are also responsible for imposing the license suspensions after a criminal conviction. That's why you received the second letter from DMV. You may notice that the first letter came from your local DMV driver safety office, while the second one came from Sacramento. Under a new change to the law, you can get your license back after 90 days if you install an IID. DMV should be able to provide you with the information on how to set that up.
Regardless of the prior APS suspension, when you are convicted of a second DUI in court, the DMV must suspend your license for two years, however, you are supposed to get credit for any suspension that you already served on the APS suspension. You can get your license back after 90 days if you install an ignition interlock device on your car. Good luck to you.
You are certainly not the first person to be confused by the criminal case's relationship to the DMV. The nuts and bolts of it are that one suspension stems from your loss at the administrative hearing, and the other is as a result of your conviction in criminal court. Contact the Mandatory Actions Unit and they will assist you in getting a restricted license upon installation of the IIED.