I think 샐쭉하다 is a rather old-fashioned word, but in this case the meaning is probably a combination of these two entries:
(동사) 어떤 감정을 나타내면서 입이나 눈이 한쪽으로 약간 샐그러지게 움직이다. 또는 그렇게 하다.
(형용사) 마음에 차지 아니하여서 약간 고까워하는 데가 있다.
- Apparently 샐쭉하다 is the standard form, not 샐죽하다, according to Naver dictionary.
Okay, even that is hard to parse, but I think it is basically the same class of emotion as "pouting". You're unsatisfied/angry with something so you're thrusting your lips in an ugly way.
Here, -(하)니 is (obviously) not a question, but an ending for 형용사 meaning "in this manner". I think it's rather uncommon these days, and only appears in a handful of expressions.
아기가 곤하니/곤히/곤하게 잠이 들었다. = The baby is soundly asleep.
뭘 그렇게 멍하니/멍하게 쳐다보냐? = What are you looking at so absentmindedly?
가지런하니/가지런히/가지런하게 자라는 나무들 = Trees growing in an ordered row
So, 샐죽하니 is basically the same as 샐죽한 얼굴로, or 샐죽해 하며.
I'm not sure 튀들어 is even standard Korean. It might be a very old fashioned expression or a dialect. In modern speech it will certainly be 튀어들어.
Finally, 가지 않느냐 is not asking "did she go", but gives an air of conversation, and shows that the narrator found it remarkable, surprising, or maybe outrageous. More like "She really went in, didn't she?" or maybe "And she just went in! Can you believe that?"
In modern spoken Korean, you may find a similar pattern like this:
그러더니 그냥 돌아서서 (가는 거 아니겠어 / 가는 거 있지)?
= Then [she] just turned back and walked away!
Bringing it all together, my translation would be:
... 안으로 샐죽하니 튀들어 가지 않느냐.
... and then she just pops inside, pouting!