What do you think happened here? I warned them to keep the cake  in the trunk of car but they insisted that the daughter would hold it on her lap and they would manage. My fault??

No, absolutely not your fault!  Even if they had put it in the trunk and still managed to ruin it, it still wouldn't be your fault. When it leaves your hands, you are no longer responsible.  If they are asking for a refund or discount, absolutely not.

not your fault but more precautions for going forward may be needed --  you need to box your cakes if you're not already and also deliver cold from the fridge -- how old is the daughter? 

hopefully, the message board will allow you to answer here in this thread -- if not, just start a new thread --

also, the for future precautions i'm presenting are not to make you doubt yourself! they should have done what you said!

and what kind of cake? a tier cake? a layer cake? a sheet?