Can I drive….

From my understanding there is not law that limits how many jobs you can obtain. You can work for two different trucking companies at the same time unless one or more of those companies have a non compete contract that states you are not allowed to be in another contract while employed with them. In this case it’s the same owner for both companies. So if she/he can use you on one shift for one company and another shift at the other company when help is need there would be no legal argument. As another commented stated, as long as the have a profile on you for both companies for other legal reasons such as taxes, insurance blah blah then you are good.

 

Yes, provided company A shares your driver qualification and drug testing program results with company B.

https://www.fmcsa.dot.gov/taxonomy/term/14626
Now, you must be in both companies random testing pool, but you don't need a pre-employment test from company B if company A shares the results and you have been in a random program for the last 6 months or tested within the last 30 days.

https://www.fmcsa.dot.gov/regulatio...-two-or-more-employers-whose-random-pool-must

This is a great summary from Idealease.
Are You Sharing Your Driver with Another Company?