would rather,would sooner,had rather,would prefer等用来表达主观愿望,它们之后的宾语从句中需用虚拟语气.谓语动词用过去式表示现在或将来,用过去完成式表示过去.如：I would rather he came tomorrow than today.若某人愿自己做某事,would rather后用动词原形.如：I would rather stay at home today．那么、would rather之后有没有接should+动词原形的用法.

由would rather/sooner，would sooner，had rather，would just as soon，would prefer等结构引导的虚拟语气，其句型结构如下：
与过去事实相反 would rather/sooner…谓语动词用had done
与现在、将来事实相反 would rather/sooner…谓语动词用did
Would rather+从句是一个常用的须用虚拟语气的句型：would rather+从句（谓语用一般过去时），其意为“宁愿……, 还是……好些“（more willingly）。
如：John wants to see you today.—I would rather he came tomorrow than today.(句中came 不是表示过去而是表示将来)
Look here,sir. Wouldn’t you rather I was out of this? (句中was表示现在)
又如：Would you rather I did it?
I’d rather you posted the letter right away.
如果表示过去的情况，则应该用过去完成时：I would rather +从句（谓语用过去完成时）。
如：I would rather you had been present.
I would rather the teacher had given some advices for my son.
与would rather类似用法的句型还有：I would sooner…, I would just as soo…, 等。
如：I’d sooner she left the heavy end of the work to someone else.
I’d just as soon you had return the book yesterday.

should是“应该”的意思,用于虚拟语气中基本也保持本意不变.
比如说：
You should have locked the door.你应该锁上门的（应该做但没做,表假设虚拟）
I suggest you should stop this project,我建议你终止这项项目（suggest表“建议”之意时后用虚拟语气）
would rather等表主观愿望的词后既接虚拟语气,理论上来讲可以用should.但习惯上不用,因为这样翻译过来就是“某人宁愿……应该……”,“宁愿”和“应该”前者表说话者主观意愿,后者表客观条件的要求,搭配起来逻辑上有些矛盾.
表主观愿望的词跟虚拟语气需要用助动词时一般用would,could等.一般不用should,但具体问题也要具体分析.