Are there any hazmat tanker companies that allow permanent riders?

None that I worked with. Alot has to do with customers. The majority of plants and refineries you go to have very strict security measures and procedures and more and more are requiring TWIC cards.
I wont say it's impossible but no company I've been with allows anyone but another company employee in there with you

 

The one I worked for let the wife ride, but she had to stay at the guard shack at the chemical plants.
Call around and ask:
Trimac Transportation
Superior-Carriers
Tidewater Transit
CTL Transportation
SVTN
Girton Propane Service
Schneider Bulk
If she wants to go full time with you choose a company that has lots of driver comfort features such as Tripac APU, etc. These aren't tanker though. They hire new cdl grads. Website may have "experience required" but that means the website hasn't been updated recently.
Danny Herman Trucking
Freymiller
Britton Transport
Schuster
Navajo Express
Magnum Ltd.
Jim Palmer Trucking

 

All those are tanker; you ask about hazmat tanker on this thread. I gave you two lists; tankers on one and other types on the second part.
These aren't tanker:
Danny Herman Trucking
Freymiller
Britton Transport
Schuster
Navajo Express
Magnum Ltd.

 

Girton is no go ever since merger China.

 

Read something about that, but forgot the details. What's going on there. The drivers making good money?

 

Before merger pay was the best from talking to drivers that are still here after. Now it's mileage and its decent but I made more per mile pulling reefer. It's give and take though home time, quality of equipment, and speed lol.

 

Yep, my cpm was more pulling reefers, but at the end of the week, my pay was way more with tankers.