I was recently discussing with my sister, who is building a travel website, and is planning to add a
iframe to the partner travel insurance company, so users can register for insurances inside her website.
However, the sevice's page is actually the whole partner's homepage, just with a URL parameter that indicates its coming from her website.
I argued that the user's trust could be breached if that page was simply inserted into a page on her website, because it would seem very gimmicky, since it's a full homepage, with lots of other unnecessary information for the customer, instead of something directly related to the user's intent. The user might also not notice he's dealing with a third party until it's too late, and then feel slighthy scammed.
With that, my suggestion was that the page should actually consist of instructions on requesting a insurance, and a link/button that led to the partner website, since this would be explained to the user.
Even after making examples of other related implementations (such as any online shop that uses Paypal and similar services), she still wasn't convinced that it would be the best alternative for the user.
Then I questioned myself: Is it better (from a trust standpoint) to embed a third-party's page into your own, and instruct usage, or instruct usage, then direct the user to the third-party's page?
Disclaimer: I am no UX professional, and neither is my sister. I just want to know if there's a common sense on this kind of matter, and what would be the most appropriate choice. Kudos if the answers provides some sort of source with more information.