Do they accept me with this bad driving history?

Googled the violation code show possibly you busted a traffic signal. A fine maybe?

I don't have anything on the second conviction.

With that said, your two accidents are going to be added up in terms of damage incurred and blame assigned to you by the recruiter who is considering your history. You can be Jesus walking on water saving the 5000 with wondrous and beautiful works but scratch someone's car or break a curb with your tractor trailer you are going to find yourself put out into the cold.

The one thing Im familiar with is called DAC Reports. You can request your history from them. A complete history will be mailed to you. Banks use the same thing to determine if you ever had trouble with checking accounts, retail worker theft, embezzlement etc. And so do employers.

I had a year in which I incurred a accident. It got messy but no one was killed. Two lawsuits came out of that against me in court that year. I fought em both off. That cost me three years sitting in a gas station at minimum wage until a company took a chance on me to get back on the road. Just as well because that was the time to cool off the points collected on the state license for speeding etc. Im a good boy now. But I had those three years burned into me as a time where things do get difficult if you are sloth and careless with accidents.

 

A few companies will hire you after you complete a cdl school.Some schools may require pre-hire letters before letting you enroll since you do have a less than stellar driving record.
Swift might let you attend their school.
Submit some applications and see what happens.
I read somewhere that Khan D' Kulia Trucking School in Los Angeles isn't too picky.
Get that CDL diploma and you'll find work somewhere. Carolina Cargo might hire you after you get the diploma.

 

The drivers in that L.A. "driving school" lean more toward a Red Crescent than the Red Cross......if you get my meaning!

 

Yep, I understand. That's what I heard about that driving school; they'll take anybody. Sometimes we just do what we have to do to get that diploma.
If "asruf" will just get a diploma, he'll find something making more than a cabbie.