I expressed the hope that her son would go on to accomplish what she had hoped for him in the position which he then had.

1. 此句在动词 hope 的用法上有误，且在in the position which he then had中， which he then had 属于“画蛇添足”，直接改为：in his position。

2. hope 既可用作及物动词，也可用作不及物动词。用作及物动词时，其后一般接动词不定式或宾语从句，但不能接名词、动名词作宾语，也不能接复合宾语; 用作不及物动词时，常与介词 for 连用，hope for sth. 表示 “希望得到某物”。

原句中， what she had hoped for him ，显然 what 做了hope 的宾语，结构是：hope sth. for sb. 这里 what 相当于一个名词， 典型的错误搭配。

3. 换一个词expectation 代替 hope，避开两个hope 重复。

4. 原句修改如下：

I expressed the/my hope that her son would go on to accomplish her expectations of/for him in his position.