Climbing
Although I don't know your state's particular laws, I seriously doubt that a DUI will affect teacher certification. I say this with much experience.
Background checks are part and parcel of the certification process in every state. But, a msidemeanor such as a DUI will probably require only an explanation.
Landing a job may be another matter. Most districts will conduct another background check. And a DUI will probably surface.
I have two DUI's and currently teach. I was a long time principal at the time of my first DUI. Neither has caused me to lose my job.
If you are sincere about this career choice, I think you will have no problem finding a district that will look at your qualifications and potential above anything else. I have hired dozens and dozens of teachers and only felony convictions raised eyebrows.
Good luck with your endeavors. You should be able to download such certification information from your state. Be sure to look at your state's Code of Professional Ethics as well.
Stuff happens to good people.
warren