Quoting a question at the end of a sentence which is itself a question

Solution 1:

The convention here is to write

Did she ask, "Is it raining?"

with the first question mark included and the second omitted.

See for example Jane Straus's Blue book of grammar and punctuation or Larry Trask's Guide to punctuation.

Solution 2:

As reported in Comma sense—a fun-damental guide to punctuation (Richard Lederer and John Shore, ISBN 0-312-34255-1), the question mark should be used once, and inside the quotation marks.

Did you hear me ask, "Do you think that I love punctuation?"

If the quoted sentence contain an exclamation point, then both the exclamation point and the question mark are used.

Did you hear me exclaim, "I love punctuation!"?

Similarly, both the exclamation point and the question mark are used in sentences similar to the following one:

How wonderful that I asked, "Do you think that I love punctuation?"!

Solution 3:

Taken from rules concerning Question mark usage here:

In the rare case where the question is about a quotation ending in a question, the sentence ends with a single question mark before the quotation mark.

Incorrect: Who said, "Et tu, Bruté?"?
(Second question mark redundant)
Correct: Who said, "Et tu, Bruté?"

Thus, for your example, it would be :

2.Did she ask, "Is it raining?"