Usually, when you browse mobile website on iPhone it displays correctly.
But when I put the same website in iframe and try to access it through another website,
the mobile website is stretched and zoomed out, as if it is displayed on the desktop browser.
How to fix it?
Usually a website that offers a mobile version asks which kind of client is calling the URL. Your iPhone’s browser provides that information. When accessing the site through an iFrame, the client information can’t be passed to the target website but only to the surrounding HTML that defines the iFrame.
iFrames generally are not recommended to use on iPhones.
See there:
iFrames and iPhones