Obviously, I don't know any of them, but I can offer my opinion of why she comes off differently from the others. To summarize, Dorothy had to work for most of the praise and happy things she got. (I have noticed that, when someone says something complimentary to her, she seems genuinely moved and pleased and smiles brightly. The others nod politely to compliments at the most.) They were the exception and not the rule. Dorothy wrote a gossip column a la Cindy Adams "Page Six". She reported gossip for a newspaper and covered entertainment from a different angle - get the goods on people. Those who provided good leads were treated like royalty in her columns. She could also ruin a career with bad press and telling what she knew. It was a difficult job socially; and it has been said the others on the show didn't always understand why she had to divulge things they considered private and not suitable for print. That's fine - unless it's your job to be a columnist and get the dirt. Who knows what her work environment was like. There is a lot of office politics in newspapers (more than, say the Engineering Dept at Dow Corning). She was staff - albeit glorified staff - but a hundred people were waiting to take her job if she made the wrong enemies with management. As you can see, she is a scrapper due to the job she was in. She lacked the financial independence the other panelists had. Maybe this made her slightly uncomfortable.
Next, she was in an unhappy marriage based on what has been written here and in print.
Office politics are alive and well in corporations and in movies/broadway too. But, Bennett was in charge of his company. Arlene and Martin apeared financially well off and never lacking for new work. It has been written Bennett and Arlene were from a different economic strata than Dorothy. They were also in a chummier clique (e.g., publisher has management and support - all work together to get new clients / Francis and Gabel have a circle of friends in New York theatre) Bennett and Arlene were neighbors. More togetherness due to where they live and they show up at the same affairs, albeit for different reasons. These people all networked together. Dorothy was not part of their network.
Move on to the internal psyche. Dorothy has been described as feeling inferior for her plain looks. She had different religious views than the others (she was a strict Catholic). More evidence these folks aren't coming from the same playbook. This could cause some friction and on the basis of disapproval and anger or jealousy over what they took for granted.
I think Arlene, Martin, and Bennett were more comfortable financially and socially. IMHO, Dorothy was a tinge jealous and wishful people would see her as the beautiful and sophisticated sort. Instead, she was seen as a Hedda Hopper type - powerful and out to get the juicy story. Facing such perceptions all the time, and seeing others who you wish you could more emulate, you turn a bit cold when dealing with others. You could be less forgiving and more shrill. She also appears to have a streak of the perfectionist in her. As when, on one show, her daughter said mommy told them to curtsey before leaving the stage.
That's my pop psychology for the day...