Questions & Answers about zhōumò wǒ bù xiǎng gēn qīnqi yìqǐ qù jùhuì.
In Chinese, time expressions usually go near the beginning of the sentence, typically in this order:
(Time) + (Subject) + (Adverb) + Verb + Object
So 周末我不想… is very natural: 周末 (time) + 我 (subject) + 不想 (verb phrase).
You can also say 我周末不想跟亲戚一起去聚会, and that is also correct and common. Putting 周末 first makes the time a bit more prominent, like “As for the weekend, I don’t want to…”. Both word orders are acceptable in everyday speech.
The verb 想 (xiǎng) has several common meanings:
to want / would like to
- 我想喝咖啡。 — I want to drink coffee.
- This is the meaning in your sentence: 我不想跟亲戚一起去聚会。 = “I don’t want to go to a gathering with my relatives.”
to think (mental activity)
- 我在想这件事。 — I’m thinking about this matter.
to miss (someone)
- 我很想你。 — I really miss you.
Here, because 想 is followed by another verb (去聚会), it clearly means “want to / feel like (doing something)”, not “think” or “miss”.