Oh, where do I start? I'm glad the OP has come back to engage in conversation. That being the case, I do have a few questions and observations.
The fact that they have not responded to our correspondence which sets out in detail why the charge is erroneous is not a sufficient response and their excuse that it must be another ryokan in their network is unjustified.
You contradict yourself. You have said more than once that they have not responded to you, but you also say that their excuse is that it must another ryokan in the network. Which is it? It seems that there may be more going on here than you're telling us.
Also, you keep throwing around terms like fraud, dishonesty, and cheating, but I've yet to see you post one concrete example. In one case, you were charged for two orders of a menu item when only one was delivered. Did you in fact order two of the items, and perhaps only one got delivered? This happens all the time in restaurants. In another case, you said that your restaurant bill was switched with another table's. Which category do you think this fits into: fraud, dishonest, or cheating? What would the restaurant gain by this? Both of those sound like they could easily be honest mistakes.
The dishonesty is epitomised by the erroneous transaction of Motonago ryokan that make the false claim that the payment must be for another ryokan when we clearly did not stay at another ryokan and they cannot claim that it was another establishment within their network as they operate independently. They therefore have no reason to hav deducted the unauthorised transaction from our account.
Now I think we may be getting somewhere. Based on what you say above, it sounds like you contacted the ryokan you stayed at, and their response was that they made no such $200 extra charge, and either in anticipation of or in response to a rebuttal on your part (which probably would be along the lines of "Well, the fact is that there is an extra $200 charge on my credit card statement"), suggested that perhaps another ryokan in the same chain made the charge. You claim this is impossible, as you didn't stay at any other ryokan. Well, it might be possible. Did you by chance make a reservation with a credit card guarantee, and perhaps show up at the wrong ryokan (perhaps because it had the same name)? Or, perhaps the mistake was not yours: you could have made the reservation through an online booking agent who made a mistake and forwarded your reservation to the wrong location. In either of those cases, the other location would have no idea that a mistake had been made, and would just think that you were a no-show, and might have charged your card for the guaranteed amount.
What I describe above is entirely plausible, and happens all of the time. It should be easy enough to figure out: call your bank and see if the merchant account was the same. Or, even before that, just look at your online or paper credit card statement: is the merchant name and location identical for both charges? If they are off by even one letter, this is a clue that what I suggest may be the explanation.