You can get on a plane with additional screening if you don't have ID. Allow yourself some extra time. Explain the situation and they'll give you additional screening.
FYI, your expired driver's license won't be accepted by anyone. It won't get you into a bar, car rental, etc. Nobody accepts expired ID's as stupid as that is. My guess is that the powers that be don't want people handing expired ID's off to others to be messed with, another picture put on, etc.
She no longer travels or drives. SS card and voter registration card, which could be used to obtain new ID were in the wallet. Why does it have to be so hard to get a replacement ID?
She's 98. I should damn well hope she doesn't drive anymore. I think they make getting ID difficult as a way to deter people from getting ID in someone else's name. I'm sure there's a way to get her back on track with the ID she needs. That said, I don't recall ever seeing anyone that old getting on a plane....ever. I realize your frustration, but I think she'll be able to get by for a while without ID.