2 differently themed front pages

so lets call the different front pages, pageA and pageB. I go to your site, which page loads? why that page rather than the other page?
I dont quite understand the question maybe, but can you elaborate on the idea behind your thinking please? It’s unclear to me how you could achieve this unless there is some kind of rule that says: if condition 1 is true load pageA but if condition 2 is true load pageB

One of the pages will be embedded in an iframe on a another site that has different design constraints.

That may be possible. To be honest I have never thought about that idea before. Good question ! I dont think there is a server side check that will tell you if a page is loaded in an iframe. I think there is only client side checking on that. I think only the browser could check on that not the server
Is this link any use to you

https://stackoverflow.com/questions/6662542/check-if-site-is-inside-iframe

Can you not just host the second website differently, then link that in the iFrame’s URL? That’s how it’s done on the WordPress themes directory.
E.g;
On this page https://www.ads-software.com/extend/themes/twentyeleven there’s an iframe that links this page in https://wp-themes.com/twentyeleven/

Thanks a lot! This will work.

oh cool