从你所问的问题来看,你对定语从句了解的确实不少了.是的,that一般情况下,用作关系代词在定语从句中作主语,宾语或者表语；when是关系副词,在定语从句中充当时间状语.但是,如果先行词是time,并且在定语从句中缺少状语的话,也可以用关系词that,尽管有的语法家认为不规范.这时的that被看作是关系副词,大多数的情况下省略.如：By the time(that) he was ten,he had learned about 1000 English words.
但是,先行词是day的情况下,that用作关系副词的情况更不被人所接受.所以你在做题的时候
,尽量的不要把它看做关系副词.
顺便说一下,that用做关系副词的情况也有的.如：I don't know the way (that /in which/--)he speaks to his father.