You are right. Your mother is a very unhappy person. It also sounds to me like she is frightened. She is unhappy but she is afraid of finding out why. She casts about for reasons outside of herself (blaming, holding grudges, looking for reasons like not having a job) because she is afraid that something inside is wrong.
Instead of being angry with her and fighting with her, see if you and the rest of the family can have a more compassionate approach. Fighting and trying to solve her “problems” hasn’t worked so far and won’t work no matter how many times you do it.
Instead of urging her to go for counseling, I suggest that your dad be sympathetic with her distress and try to get her to see her physician. There are a number of medical problems that can make people feel depressed. If the physician doesn’t find anything wrong, perhaps she will suggest counseling. Your mom may be more willing to listen to her doctor than to family members.
I understand that the fighting is stressful. Just a reminder: When someone invites you to a fight, you can always decline the invitation. One of my teachers used to say that the best way to avoid a fight is to take the “sail out of someone’s wind”. He used the image of a sailboat to show that if you don’t respond in anger (take your “sail” down), the person’s “wind” of anger doesn’t make the fight go on. So instead of defending or rationalizing, just say something like “I’m sorry you are so upset. What can I do for you?” or “I’ll try to do better”. or “I’ll think about what you said.” Then smile sympathetically and make an excuse to leave. If she won’t “let you” leave, just repeat your sympathy and then quietly nod and smile. She’ll probably run out of “wind”. People generally don’t keep going with something if it doesn’t pay off.
I hope you and your siblings and your dad can work together to stay out of fights and be more sympathetic. Your mom really does need help, not blame.
I wish you all well.