I'm sorry this happened to you. You attempted to provide an affordable product to a client at a "Walmart" price. You ended up accidentally getting it evaluated on a "Lord and Taylor" standard. It's not fair. The quilt shop seems to have been "snarky", to say the least.
First, stop trying to defend yourself. Don't send her any more emails - none. Stop it right now and go into "stop the bleeding mode". All you want at this point is to get out of the trap with the least amount of damage to you. Forget about the cheese. There isn't any. It's going to cost you. You lost money on this deal and learned some very costly lessons.
Send the registered letter with what you are willing to do carefully outlined. You might have someone edit it carefully so that it says exactly what you want to say and no more. Do this immediately. Then, don't say or do anything else. (Don't engage with the quilt shop until this is over and done.) The ball is then in her court. Wait to see what happens. (Remember, no more emails.) Then do exactly what you said you would do as quickly as you can and be done with it.
I recently retired from running a small business that depended on the internet for clients. You can't win this. The best you can hope for is a draw.
If you need help with the letter, PM me.
By the way, it's a pretty quilt.
bkay