We certainly can’t stop you from trying Discourse in an iframe but as cautioned in other topics… it’s expected to be fragile and problematic… and we don’t intend to spend time solving iframe related issues.
It might be a better use of time to describe in detail the problems you run into when theming Discourse so we can help and/or improve the process. We’ve improved theming a lot over the past couple years, and it’s something we definitely want to support and improve where possible.
There are elements that are definitely trickier to customize than others, the header being one of them. This is because a Virtual DOM was implemented to improve performance (A tour of how the Widget (Virtual DOM) code in Discourse works).
So if you’re looking to insert content into the header, you’ll need to utilize that system rather than adding content before/after it from the admin UI (covered a bit in the advanced pluginAPI section of Beginner's guide to developing Discourse Themes). There are also some good examples of manipulating the header content in existing theme-component like Custom Header Links.