Is "Should be *ing" a valid English phrasing?

I'm Portuguese and my girlfriend German. Because she is a Germanic-language native-speaker, she is constantly correcting my English. Though, often it is annoying that she corrects me in grammar constructions that I take as valid in English and Portuguese, but not in German.

Are "we should be going" or "we should be eating" valid English phrasings?

Solution 1:

Absolutely. We should be going can be a recommendation "we" be going (We should be going, or we'll be late) or a statement of likelihood that "we" will go (We should be going to the concert if all goes well).

Solution 2:

Yes. That is correct. A verb followed by -ing may be used as if an adjective to describe what the subject is (or in this case should) be doing.