I agree with the above that she's not going to be happy with anything at this point, she just seems like she's being nasty, 'Walmart would give me a refund,' she didn't order a cake from Walmart, she ordered a custom, freshly made cake from you-honestly I wouldn't see Walmart giving her a refund either! And they'd require payment upfront.
I'm so sorry your in this position! How much do they owe you, if you don't mind me asking? Personally, unless you really believe there was something wrong with your cake, I would give her the 48hrs or it goes to collections, as stated above.
Its ultimately your decision, and I understand you don't want anymore backlash and just want to get paid and put this ridiculous mess behind you. So what was the original deal you mentioned-if she ordered so much $ worth she recieved a discount? Was it a special or something? I ask b/c you said if you discount the tier she's having issues with and reconfigure her bill she is no longer eligible for discount. Ok but you forgot to add the delivery charges to her contract, but then stated it in an invoice that she signed? I hope this doesn't sound rude! I'm just confused lol. I think you should definitely charge her for the delivery! However, if you gave her an itemized invoice/contract without the delivery charges and go back at her now with them I think you'll have more complaining from her end, which could delay your payment. Does that make sence?