You say that you have the SS# so that means also a USA passport. It should really be no problem at this point, as long as there is proof of residence.
I have found the banks to be cooperative, but they may want to see the relative in person. As others have said, proof of residence in the form of a utility bill (one would be good, two would be better) will help.
I would call the utility company first. Then I would send a letter to the main office. This is just a rough idea/suggestion:
To the zzzzzz Gas company
address of zzzzzz
To Whom it May Concern,
I would like to have my wife listed on my zzzzzz gas bill. She understands that she will be responsible for the payment if I ever am unable to pay.
My zzzzzz gas bill is enclosed. I was told on the phone that we could do this by mail if I include her ID and social security
card. She doesn't speak English fluently and that is why I'm doing this by mail. Thank you.
Best regards,
Sometimes a utility company will wait until the next billing cycle to add someone to the bill. So it probably will not be immediate.
The other idea I had is that when the social security card arrived (if it arrived at your residence), it would have her name and the residence printed on the form (this is the form that the card arrives on, and then you separate the card from the form). It could be helpful. I'm not sure if you had it sent to you or not.
Good luck.