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The sign-up bonuses typically must go into the frequent-flyer account of the card-holder. So if your wife can obtain credit cards with mileage bonuses, she would also have to open a frequent-flyer account in her own name. Of course, miles in her account can be used to obtain award tickets in your name, and vice versa.

Keep in mind that both AA and UA offer one-way awards, so it's possible that you would obtain two tickets to Hawaii with AA miles, and two tickets from Hawaii with UA miles, depending on award-seat availability, and which credit cards you end up getting.