Your wife will have upgrade priority as a gold. I think you can request your itineraries be "linked" but that doesn't really do anything if your companion already has status, since they clear at their own status level anyway. (If they didn't have any status, you can link the reservations and then the companion would be able to be added to the upgrade list, but at last priority.)

You only go on the list both at the higher priority if you are booked on the same reservation, which isn't possible if you're booking tickets with different payment methods.

You could request regional upgrades for both of you, if you want. And I think under the new rules, if your upgrade clears in advance, or if it's looking good on the gate upgrade list, you could apply an RUC just for her and rely on your status for your own upgrade. (Though if you're doing it because you look good on the gate upgrade list, keep in mind that applying an RUC to her will lower you one notch on the list.)