It's been said that "timing is everything," but unfortunately the timing of your DUI and your move is terrible. You face a nightmare of bureaucratic hassles and difficulties with your driver's license in both states.
If you retain a private criminal defense attorney, that attorney can handle your DUI case (and DMV Hearing) without you being present anywhere in the state. The court (judge) will allow you to complete your court-ordered requirements in another state as well.
The PROBLEM lies with the CA DMV. IF they suspend your license based on the hearing and/or a DUI conviction they will only restore your license upon completion of a DUI Class in California. Otherwise, you'll need to complete a "1650" waiver after you move and agree to NOT drive in CA.
In my opinion, if there's anyway to delay your move for three to four months, your life will be infinitely easier.