Bad reference from PhD supervisor My PhD supervisor and I didn't really see eye-to-eye on a lot of thing but I had thought we got along well anyways. I have graduated and have decided that academia isn't for me and I want to go into the private sector. I am having a very hard time finding a job, and I am not being picky. I am applying to industry scientist jobs and also for positions like sales reps or administrative roles. The truth is I am desperate.

Although I don't get many interviews one of the places I got far along with checked my references and said my PhD supervisor said she couldn't recommend me for the position, as I had problems with communications skills. It may be true that I am awkward, but I don't think that I am that bad. I also have my MSc supervisor as a reference and another professor in my department that worked on a group project. Now I have asked my department head to be a reference as he was also on my committee. Each of these people seemed happy to be a reference but so did my supervisor.

Is it a red flag that I don't list my supervisor? I can try to talk to her but I don't know what to say. I feel like my life is falling apart, I have to get my parent's help to pay rent and I'm worried my girlfriend will break up with me as it has been causing a lot of stress.

What can I do?
Given what you describe, I think you better not include your supervisor. Her recommendation will be the most dominant because she knows you the best. Given that in the best case you will get a mediocre recommendation, and in the worst case even a bad one, it is not worth it to include her. 

Do not include her, but be prepared to explain why you do not include her. This explanation should be convincing, but not too damaging for you. For example, if you just say that you had conflicts with her all the time, your potential employee might conclude that you are a conflicting person.