Combining "whether ... or" and "if" clauses in a sentence

Question

"We can’t tell whether he did 'this' or 'that', or if he was on vacation."

As far as I know, a "whether ... or" clause can typically be replaced by an "if"-clause, which is often just a matter of style. Now, considering the example sentence above, would it be okay to write it like this? The first clause would allow me to distinguish between 2 options ("this" and "that"), which is why I'd prefer "whether ... or" over "if."

Alternatively, would it be better to rewrite such a sentence, for example:

"We can’t tell whether he did 'this' or 'that', or whether he was on vacation or not."

Answer 1

We can’t tell [whether he did 'this' or 'that'], or [whether/if he was on vacation (or not)].

Yes, generally (but certainly not always) the interrogative subordinators “whether” and “if” are interchangeable in subordinate interrogative clauses. “Whether” is more formal that “if”, and since it’s a coordination of two clauses within the same sentence, I think you should be consistent and use “whether” in both clauses.

Adding “or not” is sometimes obligatory, sometimes optional and sometimes inadmissible. Where the subordinate clause contains alternatives, as your first one does, “or not” is inadmissible. In the second clause, it is optional.

Whichever version you choose, the meaning of your example is:

“We can’t tell the answer to the question ‘did he do this or that?’, or ‘was he on vacation?’”