So this is my first order I have gotten, but because of things on both ends, it will end up with her having the cake and cupcakes about 2 days before the party. Is there anyway I can package them for her so that they stay fresh and the icing stays as desired? 

Probably the best would be to have the customer freeze them; take out the night before or early that morning.  Depends on what icing recipe you are using.  If no room to fz, then refrigerate.  They should be boxed which is then placed in a plastic bag.