When doing testing on such quasi multi lingual sites in the past I found there was nothing more annoying to users than when they were presented with a lovely traditional language selector only for the available pages in their language to be a mere fraction of that available in the major language.
There are two solutions that stand out as a good idea to me-
1: Follow the traditional route of a true multi-lingual site however clearly mark where certain links are not available in the minority language. This should be done before the users have even clicked on them- a page to say “This is not available in English!” doesn’t cut it and is only slightly more annoying than if that link went straight to the Spanish version.
Have a list of links as you would on the Spanish version but have a big clear note saying “Limited information only in English!” and then either greyed out links for those that aren’t available or a clear little “Spanish only!” note next to them.
The key is to let users know what limited options are available to them from the get go rather than having them waste their time clicking into pages only for nothing to be there.
2: Follow a route where the majority language site and minority language site are clearly differentiated from each other, they are pretty much different sites with only minor stylistic elements in common; Make it clear to the user that what they see here is all they will get in English though maybe also be sure to include a page that gives a nice guide to possibly useful stuff in Spanish (maps for instance could be good even if you don’t know the language).
This route gives less effective end results than route 1 I think and can often have quite an amateurish look but nonetheless it stands out as much better than misleading users into thinking they have a fully featured English language site.
In Japan lots of local governments follow this route of having the majority of their page in Japanese with a big clear “Information Portuguese, English, Chinese” (written in those languages) button somewhere on the main site.
This then typically goes to a single page with a directory containing links to the few snippets of foreign language information that is available (ideally I think they could be improved by also clearly noting and linking to possibly useful Japanese stuff, but foreigners aren’t given that choice)