Firstly, I am not defending the embroiderer in this case in any way.
But, it appears that there has been a communication error somewhere in the process from both parties. The original instructions given to the embroiderer may not have been explicit enough as to location, size etc. Was a sample of a previous job provided, that can be a great help. The embroiderer hasn't confirmed location and orientation of design.
We (embroiderers) are not mind readers, although some customers think we are judging by the instructions they provide at the start of a job.
I have to ask so many questions at times, that some customers get upset and accuse me of not knowing my job.
You ask a customer "Where do you want the design placed?"
Response "Wherever you think is good."
That doesn't help me. Little things like, do you want it on the right or left side? Response "What is the usual place?"
I then tell them it is personal preference.
I then have to pry the information out with more questions to finally get the location, you would think it was a state secret in some cases.

Then go through this process again, sometimes, to get thread colors.
I had a job about 5 years ago for 70 shirts, we were just doing the embroidery, job came through a third party.
I did the design and emailed sample for approval. Received reply that all was good and to proceed.
I did the job and sent it off. Was paid by the third party, all was good.
A couple of days later, was informed customer had rejected the order.
Turns out, the word "Environment" was spelt "Enviroment" and no one had picked it up until now.
Initially they wanted me to foot the bill for the lot, I told them I had the approval and it was not my problem, however I was prepared to redo the embroidery for nothing, but not pay for new shirts.
They agreed with me doing the embroidery for nothing and the third party pay for the shirts.
I only did the second lot for free, as I had billed out and been paid for the first lot
If I didn't have the approval, I would have been up for the lot.
Take the offer of free embroidery and eat the loss and put it down to a learning experience. Just lucky it has cost a couple of hundred and not a couple of thousand.
If there is no approval, then the embroiderer could be up for the lot.