I've booked DH's flights on a number of occasions, especially with £:$ being the way it has been. I've been booking through Delta, no problems at all, I just enter his name under the passenger details. I'm a bit miffed that the airmiles go to him not me though, lol.
My credit card couldn't be used by somebody else on Delta's site because it's registered for online validation, which means I get prompted for a password before my cc is accepted. Check with your mom that hers isn't the same.
Loads of people travel on tickets booked on somebody else's cc, so I wouldn't worry about it.