I'm inclined to suggest your wife app for a major card such as a Visa or MC with a bank or credit union she has an established relationship with. If you and your wife insist on apping for CITI and/or Amex this is what I would do.
- App for a AmEx Gold Delta Skymiles and ask to convert to the Blue Card
- App for a CITI Premiere Pass (or other card) and convert to the Platinum Select Card
These two cards I'm suggesting she app for have less stringent underwriting. If she does app, call and do not do it online. Make sure before she apps that both companies are still allowing these conversions.