Had the same situation a few times, one time to add insult to injury they charged rooms at a nice hotel in Oakland County Michigan while we were in Virginia burying my grandmother!
Credit card companies have been fabulous the couple of times this has happened, even sent us new cards overnight to a small campground right near the Little Brown Church in Chickasaw County Iowa a few years ago.
It is frustrating, but so far, knock on wood, we have had very cooperative people at the credit card companies. The hotel did try to come back on us, till I wrote them a very long strongly worded letter with proof that they also had been had. I hope whoever used those rooms enjoyed the porn movies they charged to my account.