Hole in differential

The car is actually still being repaired, but I can ask them for a picture when I speak to them again. Actually, I wrote up the whole story for insurance purposes so there's a little more detail. I'm just trying to figure out exactly what happened and where it all went wrong. Sorry for the length:

In early June I drove on a ten hour, 600+ mile trip. I had been told by my local Honda service center, that a rear axle boot was leaking and to set up an appointment for repair. A couple weeks before the trip, my AWD service light also began coming on whenever I would drive for more than a few miles at a time. To avoid any issues on the trip, I set up the appointment for the axle boot repair and mentioned to the service center the issue with the AWD light. In a couple of days, the car was returned to me presumable fixed and ready for the trip.
There were no issues for the first part of the drive, but as we got closer to our destination, the AWD light came on again. The car also began shaking and making a slight grinding sound at slow speeds. Traveling with an infant and wanting to avoid any issues on the return trip, I set up an appointment to have the car serviced at the local service center to ensure that it would be okay for the 600 mile drive home. I dropped my car off on June 5th and a few hours later I was notified that the car was ready; I picked it up on June 6th. The invoice shows that I informed the service department that the AWD light would come on and the car would seem to shake at slower speeds. When the service was reviewed with me, the technician stated that they had †cleared a code’ and test drove the car without the AWD light coming on. When I stated that the light only comes on after several miles, they stated that sometimes it’s just a faulty electrical system or low current and that the light was not an indication of anything seriously wrong with the vehicle. They also stated that the car was fine and safe to drive.
After retrieving the car on June 6th, I didn’t drive it again until June 15th when we planned to drive the 600 miles home. About 100 miles into the return trip, the AWD light came on again and, being told it was a faulty electrical system, I continued driving thinking nothing was wrong. When hitting slow traffic, the car began to shake again and to make a grinding noise. We got off the interstate as quickly as possible and upon pulling into the gas station, the car began to grind and buck to the point that I felt like it could no longer be safely driven.

It was towed to a place where the service manager told me that I had hit something and there was significant damage to the undercarriage, including this hole. I remember actually hitting what was a piece of another car in the road some time about a month before this trip and I feel like this was the initial damage. The service manager acted like he was shocked that the previous (2nd) service center hadn't seen anything. But I don't know what would have been reasonable for either the first or second service center to have seen.

Oh absolutely, I understand not wanting to speculate on the work that a shop did or didn't do, and at this point it really doesn't matter as it's mostly taken care of. I just like to know, when things go wrong, exactly how it happened in case something similar happens in the future. And not knowing anything about cars really, I had no reference point for whether this is common or not or what to really expect from service shops in the future. I did add a couple of images too. It's hard for me to tell really what I'm seeing here. :)

Yes, thank you, this is very helpful! It does make some sense and explains why it seemed so much worse when I was in slow, stop-and-go traffic. I guess there's no way of really knowing why the car's computer would've activated the AWD system when it didn't need to be? These intermittent problems must be extremely frustrating! :) By the time I stopped my car, something had definitely deteriorated. The grinding and lurching got worse to the point where I actually thought I was dragging something underneath my car. Was that just too much power going to the back wheels? Or do you think that could have been caused by fluid loss? I attached a better, closer picture of the damage to the case if that's more helpful at all. Thank you again!

Hi, I took my car for a 20,000 service to a dealer and they called me later right before picking up to let me know they found a hole in the differential. We’ve driven the car the night before 40 miles and didn’t notice anything. Is it possible that the service shop broke the differential when doing the service which included oil change and tire rotation?