She has emails I think stating 'No, thats not what I asked for' and 'No, those arent the fonts we agreed on', buty thats about it. She's going to check her sent items for more info. I get the point about it from their perspective, but surely thats why these agreements are drawn up in the first place? If they had come to her with a contract that had provisions for design/acceptance, then fair enough, she would have to pay and I would totally agree. I can see it from both sides, but surely its their responsibility as a service provider to get these things in writing?
Point is, they didnt do any of that, and frankly their design work was unbelievably poor, very Geocities-circa late 90's with clashing colours.
The fact that they were bad designers sadly has nothing to do with this. It seems your with entered into a bussiness agreement to design a website, your wife wasn't happy with the work so is refusing to pay. That is illegal, even if your wife didn't sign any documentation, an exchange of emails will constitute an implied contract.
The main thing is just because their work was garbage and utterly useless to your wife is meaningless to this dispute. If your wife asked them to do work and they did the work then your wife must pay the fees. Unless there was some officially agreed upon satisfaction guarantee.