She had a crazy laugh because she was literally a woman on the verge of a nervous breakdown. She was definitely not happy and blissful with her lot in life,
being married to an unappreciative old geezer who ignored her and being the official drudge for the family. Her laughing and smiling hides the boredom and misery of her life, which she tries to ignore most of the time, but when Uncle Charlie shows up, it triggers just how unhappy she's been all these years as they reminisce about the good ol' days before she got stuck in her marriage to the dullard. Her crazy laughter indicates that she's on the brink of hysteria, and she
later breaks down crying when Charlie indicates that he's leaving. She's not one of his "silly" women either; Charlie genuinely likes her, since she was the older
sister who always coddled him when he was a boy.
I'm not crying, you fool, I'm laughing!
Hewwo.

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She had a nervous type of energy about her, which I can only tolerate in small doses. The scene at the dinner table, giggling about the champagne was truly annoying!

Yes I found her annoying. Her voice and all that fuss about the cake.

Yes I found her annoying. Her voice and all that fuss about the cake.

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I agree. In fact, I'm not sure Charles qualifies so much as a 'psychopath' as he does a 'sociopath', insofar as he's obviously capable of feeling genuine affection for his sister and for Charlie (okay, something a bit more than affection there), though it won't stop him from murder if that's what's required for his own self-preservation.
I think part of the attraction Young Charlie holds for him may be that she reminds him of Emma as a young womanand he may have been a bit in love with his older sister in some way, if not the incestuous one. He makes the difference he feels about women like Emma and the wealthy widows he's bedding for money quite plain at the start of the dinner table speech, when he notes how small-town wives (like his sister) keep busy with their families and their lives, as opposed to the idle, self-centered and well-off city women he's all too familiar with. Emma (and by extension, Charlie) are the polar opposites of the female type he loathes, and it's a misread of the character to think that he despises or is contemptuous of his sister.

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She annoyed me a bit. I thought the woman was borderline nuts.
Charlie's little sister was the most annoying, and the best friend (with the glasses) who kept staring at people.

She did not grow up during the Depression era. The movie takes place in 1943, and she appears to be at least in her 40's, so she would have grown up around the turn of the century (1890's-1910's).

The mother personifies the "silly women" that Uncle Charles despises and targets for extermination. She is a generation that grew up in the depression era and likely, was married young. She's not the WWII new woman who was more liberated with the absence of men at war, the young Charlie generation of smart girls who used their head. She believed in the innocence of the era, the family, and the man as the final word on everything. She was ignorant in her happiness and blissful with her place in society and her lot in life.
Ew lover, you gonna make me clutch my pearls

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She was an odd duck, but the younger kids really were the most annoying.