I'd rather you cleaned the house today.正确
would rather + 从句 (did 与现在或将来相反);(had done 与过去相反)
再如 I would rather you came tomorrow.
不可以改成 I’d rather you to clean the house today
good command of English,这个短语翻译为良好的英语水平,command的意思是掌握 的意思,
英语的良好掌握 就是 良好的英语水平