I wouldn't worry about Delta either, I don't think their safety record is any worse than other airlines.
On my last trip I booked my own flights because of the routing (was able to fly non-stop from Dublin to Atlanta) and lack of aisle seats. Of course, GCT books the lowest fares and sometimes the connections are inconvenient. I did have to fly from Atlanta to JFK to Shannon and we spent a couple of hours on the ground waiting to take off and then waiting for a gate in New York -- but that could happen on any airline.
I've been flying Delta for years without problems, can't count the number of flights, but my complaint now is that most flights are full and the seats are crammed together. For that reason I paid for Economy Comfort and was very happy that I did. People nearby could hardly get into their seats. One woman's leg was pressed against the emergency door and they moved her to a middle seat, the only other seat available in economy.
If either you or your mother are tall, I recommend booking Economy Comfort, otherwise you'll probably be all right. E.C. seats are limited -- all were taken on my flights, so you would need to do it early.