Learn Dutch: We brengen zondag thuis door want we zijn moe. - We are spending Sunday at home because we are tired.

It is part of the separable verb doorbrengen (to spend time). In a main clause, the conjugated verb (brengen) takes the second position, while the separable prefix (door) is pushed to the end of that clause.

Is there a specific reason zondag comes before thuis?

Yes, Dutch generally follows the Time-Manner-Place (TMP) rule for word order in a sentence. Because zondag tells us the time and thuis tells us the place, the time must appear first.

The second clause is we zijn moe. Why didn't the verb move to the end?

This is because of the word want (because). It is a coordinating conjunction, which means it simply connects two independent main clauses that both keep their standard word order. If you had used omdat (which also means because), it would introduce a subordinate clause and push the verb to the end: omdat we moe zijn.

Since this lesson is about dropping conjunctions to keep standard word order, can we drop want and just say ..., we zijn moe?

No, you cannot drop the conjunction here. The trick of dropping a conjunction to revert to standard word order only applies to the word dat after verbs of thought, speech, or perception (like ik denk dat becoming ik denk). When giving a reason, you must explicitly use a conjunction like want or omdat.