Do we have to mention we are a dual-career couple, when we apply?
Answer 1: Mention it right up front, or at least no later than when you arrive on campus. If an institution is ever to offer a spousal hire it will need a lot of time to arrange that extra line.
Answer 2: Oh hell no--they advertised one position. Asking for a spousal makes you look clueless and will sink your candidacy.
Answer 3: Wait until you have an offer on the table and bring it up then.
Answer 4: Draw straws right now for which one of you gives up on the academic career and gets a high school teaching endorsement.
There is no right answer. A spousal hire, especially if you are right out of grad school and not in accounting or some other hot field, is so incredibly unlikely that there are no rules. You are trying to catch lightning in a bottle.