If I have a vehicle that is owned by a trust and my adult child has an accident while driving it, can I be held personally liable in any way?

There is not enough information here as to determine that.  Generally speaking, the owner and operator of a vehicle can be held liable for injuries or damages that occurred a a result of their negligence in an accident.  Who are you to the trust?  Whay was your child driving the vehicle?  If the "child" is an adult they themselves can be held liable.  My concern is that the insurance provider covering the vehicle will not cover the driver if they were not authorized to drive the car.  They may defend but not indemnify.  Does your child live with you?  Then your insurance may come in to play depending.  Too many unanswered questions here.  Seek legal help.  Good luck.