How can you find out if an insurance company for a trucking company carries uninsured motorist insurance for its drivers if that company does not want you to know?

If you really need to know your lawyer should be able to get that info for his lawsuit. A lawsuit is really the only time you would need to know this because:

The trucking company carries Workmans Comp-insurance on drivers by law or you would be covered for injury under another policy if you were in a collision with another vehicle.

The un-insured motorist coverage is to cover all aspects of a collision caused by another person.