The correct answer is 'prefer'. The sentence should read: 'Our parents prefer to spend weekends at home'. This is because 'parents' is a plural noun, and the verb should agree with it in the present simple tense. 'Are preferring' is not used in this context to describe a general preference. 'Doesn't prefer' is singular, and the sentence is about the plural parents. 'Prefers' is also singular and used with singular nouns.