Talk about being between the proverbial rock and a hard place! This is why, when I make my booking, I always call initially once I have the mock booking made, review on the phone with the CSR and have them send me the email confirmation while still live with him/her, never had a problem doing it this way. I then (now) transfer the booking to a TA who would handle anything odd like this for me. Clearly your mom can't do that now, but I'd still try to go up the ladder here, especially since they have the dates she called. Just because she has it in her notes (I do the same thing whenever I would call) this does not mean it is confirmed with Celebrity. I would still try to move this up, perhaps you could send an email and/or call for her, having all the details in front of you. Short of them still doing nothing, there is an email address for Lisa Lutoff Perlo, the CEO and several others here in this link. Good luck I hope this all gets resolved satisfactorily!
https://www.elliott.org/company-contacts/celebrity-cruises/