Yeah, that's not a dam problem, that's a car seat problem. If the cake wasn't cold and taken directly from the fridge into a sealed box then into the car it would be soft enough that being on a tilt could make it slide like that.
How long did you let it sit?
Regardless of the little bulges on the side, the cake shouldn't have slid. The fact that it was "first noticed it upon arriving home with the cake and that it progressed form there" indicates to me that it was the way it was handled during delivery.
Here's what i would suggest, from now on when anyone is picking up a cake, impress upon them that :
1) they must go straight home with the cake
2) keep it level - that usually also means no one should hold it. A good place for the cake to ride is the passenger side floor board. most people will displace a passenger to the back seat unless it's her mother in law (that's my experience)
3) Keep it cool - and don't set it in any direct light coming through a window
4) drive slow and leave a wide berth in front so that you never, ever have to push on your brakes even a little suddenly if someone in front of you gets cut off or stops. Tell them that the stops should be so gentle, that you don't feel the car do that thing where it bounces back a little
5) tell them that the cake is very fragile and look worried (lol)
Don't spend time with them in your house chatting while their car has time to get hot again.
Good luck - very cute cake
"Look worried". HAHAHAHA!!! I LOVE THIS!