Unfortunately, I don't have any great suggestions for you. The appeal process is all there is to get your app re-instated. You could try to create a new app and use it instead, but it's very likely that will be disabled for similar reasons as well. I know you may not know what those reasons are, but if you were flagged once for something, it's likely to happen again.
I can see nothing that would suggest, that the App that allows people post content from our website, is in any way creating a negative user experience.
Looking at your site, it's obviously talking about a sensitive subject. Some of the views expressed there may not be received well when shared on Facebook (whether by a user or an admin). Once shared, users can report any posts they don't like, for whatever reason. My guess is that it is reports like that which have caused your app to be disabled.
As mentioned, I don't know what could be done other than going through the appeal process. I don't know if you can 'bump' the appeal by replying to it or adding more context, or if it's locked until someone at Facebook responds.
I wish I had more for you to go on, but I hope the above gives some idea of what may have happened.. though it's just an idea.
Thanks,
Alex