Wow, how utterly disrespectful towards your work! Looking at the picture it looks like the cake has been transported with total ignorance and carelessness.
I don’t think you should take any responsibility for transportation nor are you liable how transportation is done. In my general terms I state that, unless I do the transport or I organise transporation, the cake is accepted as ‘seen’ when leaving my premises and to be paid in full with the pick-up.
Analysing the pictures I think the filling melted and therefore the sugarpaste sagged and additional (because the inside melted) the top of the cake bumped on the top against something (like the tower of Pisa). It’s strange that the numbers broke in the middle and not at the bottom (where it would, when not fixed nor dried properly).
How you describe your client I get the impression that she doesn’t have a clue how much effort it takes to design a cake, that she isn’t organised and she doesn’t know how to handle staff/subcontractors.
All this is not your business, nor should you care when she obviously doesn’t.
My conclusion: you’re work is flawless and you should be paid in full.
And, you should take more pride in your work and the passion you’ve put and still put in your work. You have developed a very unique style and should tap yourself on your shoulder once in a while :-)
Btw: I call people like this acquaintances, not friends. My friends have similar standards of moral and values
Natascha, Zurich, Switzerland - http://www.facebook.com/fleurdesucre - http://pinterest.com/fleurdesucrech/ - http://www.fleurdesucre.ch