Under what circumstances and how should a new hire ask for a new trainer?

I would call a supervisor, and give your reasons of why you want another trainer. I don't know anything about training, but I don't know why you couldn't call the boss and ask for another trainer..

Just make the call, they should've given you a number to call for that kind of problem. Be prepared to explain in detail why you want a new trainer and you may have to wait for one too.
Are things really so bad that you can't work them out?

If said trainer asks you (or tries to make you) do ANYthing unsafe, immoral, in violation of the law, or in egregious violation of company policy. Trainers should show and instruct new drivers how to do things the RIGHT way, not how to get around doing them the right way.

Also... If the trainer HIMSELF drives in an unsafe manner! It's YOUR life at stake when riding with ANYONE else, be it a trainer or a team co-driver.

Also... if he stinks and won't take a shower, or is a bigot and won't shut his mouth!

But, like the others said.... be SURE you have a valid reason or the company will write you off as a "whiner!"

See my sigline!

First of all before you even started the truck, you and trainer should have been open with each other and talked about mutual expectations. If your trainer is a danger to your health and safety, call your driver manager. If he is not professional (doesn't shower, foul mouthed, not safe, rude, or not properly training you) talk to dispatch and demand another trainer. Over the years I have met good trainers and some that I would have packed up and demanded a new one. Your problem is not uncommon.