I'm wondering if it's possible to open a link to another site, in a frame (or by some other means), and suppress the 1-2 popups that load on the external site.
I don't think there is an easy way to accomplish this. Your best bet would be to have a page on your server act as a proxy for fetching the page from the other site, then modify the html you get back to remove pop ups. Not an easy task, but possible. As a POC, you could explicitly target the popups you know about by looking for the page url they open.