When I go to the https version of your site outside of Facebook, I run into a few issues:
www.accbattles.com/
First, I get a certificate error that the SSL is actually enabled for just:
accbattles.com/ (no www)
However, if I go to that URL, I'm automatically redirected to www. On that page, it looks just like it does within Facebook.. so it's not a Facebook thing.
My guess is that you have a few issues that need to be fixed:
1) Your SSL certifcate should be updated to be for
www.accbattles.com and not the non-www version
2) Your stylesheets are likely loading over http:// and not https://. You should have your site load them with a relative path instead of a hardcoded path using http.
I hope that helps get you started on narrowing things down. If you have any questions or issues though, just let me know.
Thanks,
Alex