I am always confused regarding the accepted placement of the question mark when there is a comment or the like following the actual question in a sentence. Consider the following options:
Shall I direct the request to you?, in which case I will proceed with sending the email.
or
Shall I direct the request to you, in which case I will proceed with sending the email?
Which one (if either) is correct? Is there a better option?
You should not combine a question and a statement together into a complex sentence.
The sentence in the question could be correctly rephrased like this:
Shall I direct the response to you and proceed with sending the email?
And, as others have pointed out, it would be correct to split it into two sentences like this:
Shall I direct the response to you? If so, I will proceed with sending the email.
But phrasing it like you do in the question is wrong. A case is not defined by asking the question in the first clause, so the "in which case" qualifier is not recognizable in the second clause. Further, the subject between both clauses is the same, so there's no reason to use two clauses. Lastly, there is no reason to combine a statement and a question together in a single sentence like this. It's never right. Don't do it.
The following recommendations (other style guides may not concur, so let's not start calling them 'rules') are given by Kathy Sieckman at the Proof That blog. Though I like the recommendations here. I've given a lengthy quote to address your general query about non-terminal-question sentences etc rather than the single example:
Short questions that fall within a sentence can ... be [and usually need to be] set off with dashes or parenthesis instead of commas....
• The new association president – do you know her? – emailed me.
• The new shopping mall – have you been there? – has great stores.
Where a longer direct question comes at the end of a sentence, start the question with a capital letter and precede the question with a colon or a comma. The question mark ending the question also ends the sentence.
• The question is, Have you completed your application for a Board position? (Direct question)
Note, however, that shifting the order of the words can transform a direct question into an indirect question. In a direct question, the verb precedes the subject (shall we, can we). In an indirect question, the verb follows the subject (we shall, we can).
• The question is whether or not you have completed your application for a Board position. (Indirect question)
See how the indirect question asks whether or not you have and the direct question above asks have you? That makes the difference in whether to use the question mark or not.
Where you have a series of brief questions at the end of a sentence, you can separate them by commas or with question marks (if you want more emphasis). However, you do not capitalize the individual questions where they are all related.
• Does the position include typing, drafting documents, and scheduling appointments? (This implies that the position includes all of these things.)
• Does the position include typing? drafting documents? scheduling appointments? (This implies that the position may include one or more, but not necessarily all, of these things.
If, however, you have a series of independent questions, you will capitalize each question and end each question with a question mark.
• Before accepting the position, you should confirm the following: Are you qualified for the position? Is there on-the-job training to keep your skills current? Is the pay in the range you are looking for?
Sometimes, independent questions in a series are elliptical (or condensed) expressions. See The Question Is What Happened to the Question Mark? post.
• Did Jim sell his Corvette? To whom? For how much? When? (This is read to mean “Did Jim sell his Corvette? To whom did he sell the Corvette? For how much money did he sell the Corvette? When did he sell the Corvette?”)
I'd still separate your example as Andrew recommends: by far the best style here. However, a parenthesis is acceptable:
Shall I direct the request to you (in which case I will proceed with sending the email)?
