I don't want to go shopping with Charles,I'd rather stay at

正确答案：I'd rather stay at home instead of going shopping with Charies.应为后面是现在分词且是两空,所以用than,应用instead of另外给你would rather的用法总结：一、 “would rather+动词原形”是英语中常见的一个惯用句式（美国英语中多用had rather）.’d rather为would（或had）rather的缩写形式.would (had)在此决无“过去”之意,且无词性、时态的变化.该句式常用来表示选择的意愿,意为“宁可……；宁愿……；最好……”.例如：
He'd rather work in the countryside.他宁可到农村去工作.
If you'd rather be alone,we'll all leave here.如果你宁愿独自呆着,那我们都离开这儿.
You would rather stay at home and do some reading this evening.今晚你最好呆在家里看点书.
二、 would rather与than连用,可构成另一个惯用句式,即：“would rather...than.”意为“宁可（愿）……（而）不要（愿）……；与其……不如……”.用以表达主语的意愿,强调经过选择后做其中一件事,而不愿做另一件事.例如：
I would rather watch TV at home than go to the cinema.我宁可在家看电视而不愿去看电影.
三、 在使用“would rather...than...”句型时,应注意以下几点：
1.than 后边也应接动词原形,但如该句型前后连接的两个动词相同,则than之后的那个动词可省去.例如：
I'd rather know that now than afterwards.我宁可现在就知道这件事,而不是以后.
2.would rather...than...也可改写成 “would...rather than...”,其用法及含义仍不变.例如：
Facing the enemies,our soldiers would die rather than surrender.面对敌人,我们的战士宁死不屈.
3.有时为了表示语气上的强调,可将rather than置于句首.例如：
Rather than refuse to help you,I would borrow money from my friends.我宁可向朋友借钱,也不愿拒绝帮助你.
4.would rather后也可跟从句,表示主语宁愿让某人干某事.这时,从句谓语动词要用虚拟语气,即用一般过去时表示现在或将来要做的事；用过去完成时表示已经做过的事或过去要做的事.例如：
I'd rather she set out to do the work now.我宁愿她现在就着手做这项工作.
I'd rather you met her at the airport tomorrow morning.我但愿你明天早上能在机场见到她.
I'd rather you hadn't told him the news that day.我真希望你那天没有把那个消息告诉他.
5.would rather后还可接动词的完成式,表示主语要做某事,而结果却事与愿违.例如：
I'd rather have left a note on her desk.我本想留张字条在她书桌上的.（事实上没有留）
试比较
I'd rather I left a note on her desk.我宁可留张字条在她的书桌上.

instead of

I'd rather stay at home instead of going shopping with Charies.

instead of