Webforward / redirect with Iframe breaks CSS

Hi,

I have a WordPress installation on link 1 (see private content) and it looks fine on Chrome browser from mobile and PC.
But the CSS breaks somehow when I access it from link 2 which is is a “webalias” in my hosting configuration panel. Which basically means it has an Iframe with in it the the aforementioned site. So the URL of link 2 remains visible in the browser, but you see the content of link 1. It’s a service from my hosting provider, and keeps me from having to pay for webspace for link 2.
So some CSS doesn’t seem to load. The fonts are not what they’re supposed to be, and on mobile the responsiveness doesn’t work, the fonts are way to small.
But the colors seem fine. I’ve attached two screenshots (in private) with the URLs visible, so you can see the difference.
Do you have any idea how to fix this? Is it a loading time problem? I’ve tried different performance settings, and my current ones are:
CSS file merging and compression: disabled
Javascript file merging and compression: disabled
Http security level for checking readability of merged files: use ssl
Disabling of template builder elements: always load all
Load google fonts in footer: enabled
Delete old CSS and JS files?: enabled

Hopefully I can fix it without having to pay for two webspaces.
Thank you!