When I was at DX courts and law firms were the bedrock of DX mail product and I would often have single piece items up to bankers box size along with actual mail. AFAIK its subscription based and not charged per item unless a signature was required / fully tracked, so for the sake of sending before 5pm and delivered before 9am, I’d suggest they send them that way.
As a young person, with her foot on the bottom of the ladder, this young lady has to tread carefully. On the one hand, she doesn’t want to cause an upset and make herself look bad to her employers; on the other hand, she wants to stay within the law.
If it was me, and the insurance cost was small, I would swallow it, but I would be looking for a mileage allowance - especially since being a car owner seems to have become a requirement for the job. This is one time where a union might well be useful.