不管采不采纳,我的回答就在这里
这里先要把定语从句：the government had ,去掉,然后,句子简化为：
can you imagine the difficulty,persuading the villagers to leave here
然后,你就发现,这个persuading 现在分词,是做伴随状语的,逻辑主语是i ,i和劝说之间是主动关系
就相当于,这样一个状语从句：
when i persuade the villagers to leave here,i can imagine the difficulty.
但是,现在发现,我这个回答,有个错误,就是逻辑主语找错了,逻辑主语,是政府,而不是你我
这个句子的结构,其实是这样的：
Can you imagine the difficulty the government had persuading the villagers to leave here?
= The government had difficulty(in) persuading the villagers to leave here,and can you imagine it?
政府在劝说村民离开这里的时候,遇到的困难有多大,你能想象得到吗?