On Tuesday, I managed to get hold of our driver's supervisor and I explained the problems. He was genuinely shocked (and not in a "I'm covering up" kind of way but in a "I know you're telling the truth but I'm having trouble processing because it's out of character" way) and said that our driver has been with them for 5 years and is well-liked by the parents and kids. He also told me that the driver had no right to put Alex in restraints without seeking permission from both the company and the parents and that she cannot simply refuse to drive him.
He said he would take care of the situation and talk to the driver. When he called me back a few minutes later, he said that the driver refusing to drive Alex had been a misunderstanding (I have my doubts about that, but given the language barrier, I'm willing to let it go) and that he'd spoken to her about the restraint issue. He also told me that he was putting a note in the driver's file so that this would be on record if there were any problems in the future.
On Tuesday afternoon, the driver still had Alex in the seatbelt restraint. I didn't say anything, just got him out and got him into the house. I called the supervisor again and left a message explaining that the drop off had gone well but that Alex had still been in the restraints.
The next day, the restraints were gone.
I suspect there will be some tension for awhile. It's not a great start to a professional relationship. But I'm wiling to let things play out as long as she remains civil and professional.