The employer might well deny promotion or fire you over it. No federal or California law expressly prohibits it. However, California has recently adopted the Fair Chance Act that bans employers from asking about convictions until after making a conditional offer of employment, and then if the employer finds out about the conviction it must make an individualized assessment that looks at the duties the employee will do in the job and whether the particular crime he or she was convicted of would relate to those job duties. The employer also needs to take into account how long ago the conviction was. While that law literally applies only to new hires, an employer would be wise to do that individualized assessment when later conducting reviews for promotion, etc.
You know your company better than I do. But in most cases I would not at this stage volunteer this information. Of course, if asked about convictions you shouldn't like about it. Lying about this stuff gets more people fired than the actual conviction does.
One other suggestion. Make it a habit to never drive after any amount of drinking. Every drink you have diminishes your ability to drive and puts you and others at increased risk of harm. Even one drink will slow your reactions and perceptions a bit. You do not need to have a .08 BAC to be guilty of a DUI. If the officer sees evidence of impairment and evidence that you had been drinking, that's all the state needs. Don't put yourself at risk for that. With two DUI convictions already, the penalties will start to really hurt if you get hit with more DUIs.

