(1) Quand utiliser "de" après "pas d'autre" et avant verbe infinitif; (2) devoir v falloir

I think Maarten is correct, and that explains why "de" is (presumably) required here, whereas in some other contexts (e.g. comparisons, as explained in the link below) it's optional.

http://bdl.oqlf.gouv.qc.ca/bdl/gabarit_bdl.asp?id=3892

1) There is a specific lesson which addresses your questions: D'autres vs des autres = others (French Indefinite Adjectives)

2) You can, of course, say nous devions aller visiter. It is more personal and less of a general "one had to go visit..."

@Chris. Thanks for your reply.

(1) The lesson D'autres vs des autres = Others (indefinite adjectives) does not address my question, which concerns the use of "de" before an infinitive, for example in the clause "nous n'avions pas d'autre choix que de  succomber meaning "we had no other choice but/than to succumb". What is the rule for using "de" after "pas d'autre qqch que [de]"?

(2) Ok.

Ah, now I get your question! The de before succombre is just a repetition of the de before autre choix. So it's there for the same reason as the first de.

Ok, so why is it repeated? Surely the "de" (or "d'") before "autre" is associated with "autre". I'm still puzzled as to the correct construction of "no other ... but" in French. For example, "I have no desire other than (or but) to learn to speak French".

I think this stems from the basic 'expression' being «avoir le choix de . . » - similar to English 'have the choice of . ." - the negation, the inclusion of d'autres (to modify choix) and the introduction of a restriction 'que' (but or than in English in this setting) doesn't change the use of «avoir le choix de + infinitive». 

Ah, now I see. It's a kind of combination of "I have no other choice than of succumbing..." and "I have no other choice than to succumb...". Thank you, Maarten. And thanks for the informative link, Alan.