I'm tired of you coming late to class every day.这句话老师说不对,应该变成your,可是我觉得"coming late to class every day"是对you的行为的补充,即I'm tired of you （coming late to class every day).或者我所想表达的的是

I'm tired of you coming late to class every day.这句话老师说不对,应该变成your,可是我觉得"coming late to class every day"是对you的行为的补充,即I'm tired of you （coming late to class every day).或者我所想表达的的是
I'm tired of you coming late to class every day.这句话老师说不对,应该变成your,可是我觉得"coming late to class every day"是对you的行为的补充,即
I'm tired of you （coming late to class every day).
或者我所想表达的的是括号里的内容做后置定语.这样理解可不可以?

I'm tired of you coming late to class every day.这句话老师说不对,应该变成your,可是我觉得"coming late to class every day"是对you的行为的补充,即I'm tired of you （coming late to class every day).或者我所想表达的的是
你觉得"coming late to class every day"是对you的行为的补充

以及你想表达的是括号里的内容做后置定语, 这两种理解都不可以.

因为be tired of doing sth. (讨厌/厌烦做某事), 这是一个固定搭配.

当doing sth.带有逻辑主语时, 其逻辑主语应该用形容词性物主代词或名词所有格,即:

be tired of sb.'s/one's doing sth.

因此, 正确的说法是:I'm tired of your coming late to class every day.

doing作后置定语时, 表示被修饰的名词或代词正在进行某动作.如:

I know the girl standing over there .

Who is the boy sitting near the window ?

因此, 如果把(coming late to class every day).理解成you的后置定语,那么它表达的意思是:

"每天上课正在来迟到的你",这显然讲不通.

另外, 如果把它理解成是对you行为的补充, 那道理同上. 同样是表达you正在做某事. 讲不通.

所以你那两种理解都是不可以的.