All the language in the world in credit card agreements doesn't mean #@^% if they dispute it. They'll pull the money back, hold it until they determine what the situation is, then either give it to you or not. They don't have to give it to you even if the cake was delivered and was exactly what they ordered. Ask me how I know.
I had almost the EXACT same thing happen to me this summer, with a heinous pair of wenches. The cake was just what they ordered, I had made the same cake for other people that week and they loved it, they claimed that it was dry and that people were complaining about it at the reception. As I put pieces together by talking to the venue and other bakers they interviewed (who I knew personally) it became apparent that they had spent too much and were trying to get money back. They were complaining to me that nobody could eat the cake, but at the same time were complaining to the venue that they cut the pieces too big and not everyone got the cake, so they wanted $$ back from the venue too.
So which was it...inedible cake, or cake that not everyone got? They were just trying to get refunds from everyone.
Anyway, they immediately "took it to the next level" by posting insulting things on my facebook page and having their friends do the same thing. Then they filed a BBB complaint under a fake name (which actually worked to my advantage because the BBB could see they were a little off). I had to ban them from my facebook page and post about the banning (without mentioning who they were) because I didn't know who had seen what on the page before I deleted their comments. As soon as I did that the bride called me (it had been her mother calling to scream at me up until then) and she agreed to a refund as long as she would pull her complaint, not post anything else online anywhere, and put her mother on a leash. As soon as the refund was accepted, they contested the entire credit card charge
I had to go through a bunch of paperwork to show that I'd refunded them (the original payment were using Square over the phone with a CC) and Square won't let you do a partial refund. I had to refund using a check, but since I had the printout of the check that wasn't an issue to show that they'd received it. Since Square is the processing party and the card used was an Amex, they couldn't give me any information about why they said it had been pulled back, Amex received that complaint and Square just processed it. In my case I showed that they'd received a refund so they did give me the money back eventually, but it was a pain in the rear.
If you used a service that won't let you do a partial refund, do NOT refund anything unless the person is there in person to charge the new charge, and charge it BEFORE you process the refund. Over-the-phone transactions are the ones that they look at hardest since they're obviously the most fraud-related. And if you process the refund first there's no reason why she would hand you the card to re-charge her for the balance.
I have a friend who just went through this with paypal, and they said that unless there's a shipping label proving that the item was delivered they can't take the vendor's side on disputes. The guy she talked to said that cash only is the best way to go for a business like this where the product is eaten, because they can't take anyone's word that the cake was or wasn't edible. That isn't realistic based on how most people today use some form of credit, so things like this are going to happen every now and then. I actually wrote a blog article about this exact thing tha's going up next week, I think...
I've noticed a huge increase int he number of complaints regarding people who want refunds in the past year. In the 14 years I've been doing cakes I can think of 4 refunds I've given, and two of them were this year. In both situations there was nothing wrong with the cakes, but the client was obviously trying to recoup some of their costs. I've spoken to a lot of diferent wedding pros who are seeing the same thing, too, it isn't just me. I think that people are watching the tv shows with million-dollar weddings, then when they go to get the same thing thye're hit with the bills afterward and realize that they can't afford that, so they start complaining.
The ability of people to go online and slam you without any proof is giving certian less-than-honest individuals the ability to strong-arm their way to refunds that they don't deserve just to shut them up, but with certain people that's the fastest way to get rid of them. To make myself feel better about it, I did figure out that after all of my expenses I still made about $50 an hour on the cake for those two wenches even after the refund
I'd also tell you that with this woman you should take everything to email so that you have it in writing. Find the person who's more reasonable and deal only with them. In my case the bride was the more reasonable one, her mother literally screamed at me, and I refused to talk to her after the first phone call. Get their correspondence in writing in case they do dispute it.
I'd also call and talk to the venue to find out what really happened. I always call and talk to the person who actually cut the cake if there's a question about anything.