Sorry about your car. We have a towing business and I'd say that driver was extremely nice, you should give him a positive yelp review! Oddly, we've seldom encounter tows with dogs, a few times we'd had them stay in the vehicle, but the other scenarios are sad because law enforcement is involved and they call out animal control before we tow.
When I called in Triple A I made sure to tell them I had a dog with me and asked if would be a problem, so I could make other arrangements if needed to pick us up. Thankfully they said not a problem and tow truck driver was very nice and gracious about it. I will for sure give him a positive review with Triple A.