1. Whom would you rather _______ the work?

答案是have do。本题涉及 have sb do sth 句式，本句的陈述句为：

I would rather have sb do the work.

如果就其中的 sb 提问，即为：

Whom would you rather have do the work?

2. What’s troubling them is _______ enough experiencedworkers.

答案是their nothaving。动名词的否定式应将 not 置于动名词之前，如果动名词带有逻辑主语，则逻辑主语置于否定词 not 之前。又如：

To think of his not knowing about it!  想想看，他对此竟然一无所知。

It surprised me your not remembering my name.  你不记得我的名字，我感到意外。

I understand your not wanting to discuss the matter.  我理解你为什么不愿讨论这件事。

In case of my not being here, ask my brother to help you.  如果我不在可让我弟弟帮助你。

The trouble was their not being able to agree amongthemselves.  麻烦的是他们自己不能取得一致的意见。