To share a possibly similar accident story. My daughter drives an '07 Acura RDX. She got rear-ended twice in a single accident as she was the first car in the line & successive cars rear-ended each other. It happened exactly a year ago this month so it's still fresh in my mind.

Her car seemingly appeared okay other than a banged up bumper. She drove to her apartment after the accident....no problems. Later in the day drove to campus for a class, went over a speed bump and the driveshaft fell out of the cradle onto the road & the transfer case spilled all it's fluid. Imagine if she had parked the car for the rest of the day & then headed out on the interstate what could have happened.

I know yours is the tranny, but oh yeah it was definitely the accident and the other drivers insurance company owes you a repair job. Fortunately, I didn't have to argue too much with the adjuster, he could see the cause and effect. Good luck.