Had a quick look and the only thing I can identify as a problem is that you have JCH-optimzer active; make sure this is not the case when using Autoptimize as combining optimizers can cause problems.
More generally speaking: first and foremost try to identify what is breaking your site by just disabling CSS or JS optimization. Once you know that, dive in and try identify what code/ files (CSS or JS) are responsible for the broken feature and try excluding that. If the problem is with JS, chances are you’ll find useful information on your browser’s developer console.
There’s more info in the troubleshooting tips and info on exclusions in the AO FAQ.
Feel free to follow up here with info on what you find, I’ll be happy to assist
hope this helps,
frank
