If you're going to the vet tomorrow the treatment will have to be your decision. I am in no way qualified to advise you on the treatment. The only thing I can do is make some suggestions that you might consider. I think one of the main things I would be wanting to know from her is if she has had the opportunity of treating the Feline Rolling Skin Disease. I know from talking to my vet last Tuesday that in 15 years of veterinary work she only ran into it once, and luckily she had a vet from southern Ontario that recognized it, and was able to address the problem. I don't remember what was used but I do know it wasn't prednisone. If all else failed I would be looking at the prednisone but as a first option I think it is a little over-the-top to start off with. It used to be prescribed when all else failed. I think I would be calling around to some different offices in the area telling them what the conditions are and finding out if they've had any experience with FHS, and getting a 2nd opinion.
When it comes to cleaning detergents and so on there really isn't too much you can do other than being aware that they can cause a problem, and try to limit their use where possible. Try to find something that is a little more pet friendly, and stay away from the harsh ones like Pine-Sol and Javex if possible.
I am again enclosing some websites for you to have a look at. They will explain the healing conditions of coconut oil and its applications. My findings to the Rolling Skin Disease and coconut oil was strictly by accident. I was just looking for something to stop the shedding and dandruff among the cats and tried it. It worked well plus the bonus that Yogi is now enjoying no FHS although he will have the odd twinge from time to time. The conditions just subsided from being severe and often to being far and few between and short in length and severity.
I never thought to ask what you're feeding Binky. Quality food will have a lot to do with it and preferably canned. Raw is even better but that's another story plus a stress problem you don't need right now with Binky.
The 2nd last website has a video you might want to watch, and the last website will give you some ideas on treatment.
Hope this all helps. Be waiting to see how you make out best of luck.