Your MIP charge will not affect your DUI.
DUIs in California are good for 10 years - stay sober when you drive - the consequences escalate with each conviction.
A standard first DUI in CA is, usu, 36 months summary probation (unsupervised, just don't pick up another offense) a fine of $390 plus penalties and assessment fees (usu 1500), the 3 month alcohol program [SB541}, and a suspension of your drivers license by DMV (usu 4 mo). [A first time DUI carries a potential of six months jail and a fine of 1000. If you screw up and get a probation vio for not abiding by the terms of probation, the Judge has up to six months of county jail he can sentence you. In many jurisdictions, no additional jail time is ordered (other than the one day on arrest/booking); some are sentencing 48 or 96 hours of county jail for a first.
Within 10 days of your arrest, you must notify DMV if you wish to appeal the suspension of your DL. You will go before an 'administrative' 'judge' - a DMV employee.
DMV consequences are separate from the court consequences. They will require proof of the completion of the alcohol program, and insurance proof, and you must pay a 'reissue' fee to regain your DL.
You can hire an atty & try to fight this. At .14, you do not have a 'rising defense'; an atty can demand that the Prosecutor prove the checkpoint was set up according to required procedure: an avenue allowing people to get out of ckpoint and random selection of vehicles and proper notification to the media. Ckpoint requirements are standard and most police agencies are adept at following the necessary procedures, but
Who knows ? Maybe they slipped up ?
If you don't want to fight the charge, I would recommend using the Public Defender (if you qualify) or appearing 'in pro per' (representing yourself) at the arraignment and plea. Ask to speak to the Prosecutor about your charge and ask them what they want for a No Contest plea. Don't speak about the facts of the case (they can be a witness agin you); just ask for an offer to dispo the case.
If the offer sounds excessive, ask for a continuance to consult an atty & then see what they say you should normally get in that court.
PS: some counties allow you to serve any jail time in 'private jail' (companies run the jails for some cities - they charge about 80 per night) Your county may, or may not allow this. It is a safer environment to do jail time.
Good luck.