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Well you have the age with your cards, I would get your utlization down and if your wife's cards can't be paid down, you might want to remove yourself, but I will let others chime in in regards to that.
Do you have any negatives, your scores seem to indicate you may?
From my point of view, her cards are doing nothing for you, actually dragging your scores. None of hers are older cards by any age, and to make that count, would need to be several years older.
Her utilization, is also dragging down your scores. Unless she paid way down quickly on all accounts, and yours a bit more <28.9% utilization, you will most likely be denied for any new credit.
Reduce your utilization, remove yourself as AU on all her cards. Keep low and timely payments on yours, Discover will eventually graduate to unsecured. From what I see you just let your accounts age, and prove good utilization and payment history. Within a year of your youngest, your file will improve considerably. Apply for none in the meantime.
If you have any derogs, late payments, collections, chargeoffs, those accounts are what you need to focus on during this year time length.