The sibs had it out during Thursday's episode of their Hulu show, where Kim confronted Khloe for her condescending tone. As the family was set to head to Aspen on vacation, Kim wanted to clear the air ... but instead ended up firing off several digs at Khloe.

According to Kim, Khloe judged her for not washing Chicago's hair, taking it upon herself to style the child's 'do. However, Khloe felt the criticism was unwarranted ... accusing Kim of projecting her insecurities onto her.

She added ... "It sounds like you're dealing with a bunch of your own bulls*** and you decided to harvest this and build up all this animosity towards me, when this is a you f***ing problem."

Though Khloe assured Kim she wasn't trying to shame her, she refused to engage in the drama ... telling her sister to "slap me or something" and get over it.

As you can imagine, that only served to ratchet up the animosity -- watch the clip, as Kim slammed Khloe for having "a stick up [her] ass" and only spending time with family.

As Kim put it ... Khloe needed to get laid to break out of her rigid schedule -- prompting Khloe to call Kim "a petty little bitch."

And, of course, all this drama carried over to Aspen, where the sisters hashed it out again in front of their mom, Kris Jenner, and sister Kendall Jenner.