I know and understand how you're feeling on the defensive and also wanting to dig your heels in a bit because of the Mom's behaviour.
There are essentially 2 reactions you could have to this whole affair., 1) feel instinctively bad and want to return money or compensate somehow, or 2) stubbornly insist that you will NOT refund any money because everything was fine when you left.
It sounds like you're having some feelings of self doubt- forget how that affects a possible law suit or how that affects the mom's next move.
Do your homework. Because in a legal situation this is what you would be asked to produce. Pull out the contract. Sit down and write EVERYTHING that has transpired from the first consultation to now- be civil and factual about it- this is a description not an opinion piece (ie I think the Mom is a ahem lol). You're merely stating facts, a completely detailed recount of events. The evidence would prove itself that she's been lying about a bunch of s tuff. No need to say 'she lied this time and that time' - just report what she said and when, what the bride said and when.
When you set the cake up you have to honestly ask yourself why it was leaning - remove all the feelings you have as a result of this 'attack on you' -. Find pictures., Go to the wedding photographer. Go directly to the source to get information and write this down. Do not rely on someone who heard someone else say. You also have your own photo.
Meanwhile, in legal interest, she has threatened you or made you feel on the defensive, however it IS in fact her job to provide proof of what she's accusing of. IF she has no ground to stand on, ie re you already feeling when you left that it was leaning some. You really have to be honest with yourself asking yourself why it was leaning. If it was a support issue then as was mentioned a few times, the compensation does fall on you- however you can handle that a number of ways. Good luck with that.
Re: legalities of owning a business/baking out of kitchen, again do your homework. March right down to the government office in charge or call, and ask, and take notes, and find out what you need to be running a business out of your home.
Ask a lot of questions, write a lot of unbiased /factual notes. Who signed the contract? What does the contract say.
If you are not in fact legally entitled to run a business out of your home, I would do as was mentioned and immediately figure out a way to refund money or compensate amicably so she doesnt think you're a pushover or think you're refunding because of her bullying or threats about your lack of business licence. Do not bring up the lack of business licence to her (if that is actually an issue- let it alone - if you are not legal, then quietly refund the money and be done with it. Then MAKE HASTE and get yourself the proper licencing and insurance before you even TALK to the next potential customer.
Good luck, and remember keep a level head in all this.
I dont have any wedding or other cake contract experience but I took a lunatic landlord to residential tenancy court' a few times and we did our homework/provided unbiased evidence/photos and let the evidence speak for itself and the arbitrator just watched him foam at the mouth and it was open shut case for us. But we left out our opinions of the whole thing. That's REALLY important. Not always easy to do when someone is attacking you but assessing everything honestly and factually is important
The cake is gorgeous by the way!