間vsうちに and some examples


To be honest this has been pretty confusing, via a grammar book im reading it
says

> When it indicates an interval of time, aida refers to the 'time space'
> between two points, i.e the beginning and the end. In other wide aida can be
> measured in clock time, uchi however simply means 'time space within'.

Then in the following examples

子供が学校にいっているうちに（間に）本を読みます

雨が降らないうちに(間に here is wrong) テニスをします

冷たいうちに(間に here is wrong)ビルを飲んでください

I really dont understand why the last two sentences are incorrect with 間に and
not sure how this really relates to `clock time`, any help or even more
examples would be appreciated.

