幫幫手CHECK一下GRAMMAR

01
will ... willing不對
如果你必須要用willing(願意)這意思加在will(將會)之後，可能要改變句子的寫法。如果用willing則不會用will而改用is來表達確定性。但如果像你全句是附帶條件性話，最好是用will help便可以了。不能把未知數加確定的用詞同時放在句子的構成上。
perfectly willing亦不太合邏輯，因為perfectly去做或決定一樣事是帶著已成事或完成了而說的，但你全句的更定性卻不太強。
great pains雖然這phrase本身未必錯，但跟句子的用意有些出入。你可能是想說努力/用力/有難度，不過說服人的說法一般會用great lengths以表達要花時間和耐性而不是把重點放在你個人的力量或面對的難度上，當然你是作者是可以選用的。
但我會寫成
Being a sensible person, your mother will certainly help the woman as long as you spend great lengths to persuade her to do so.


02這句不太明白你想講的用意和處境
如果沒估錯那advice是to get better understand of the root of problem
句子上還有一點漏洞，以下是我的修改
The second piece of advice is that you should better get to understand the root of the problem.

"take great pains to persuade her" is totally acceptable, meaning putting a lot of effort into persuading her.

Usually we say "go to great lengths to do something", also meaning putting a lot of effort into doing something.

01. Being a sensible person,your mother will be perfectly willing to help the woman as long as you can persuade her to do so with great patience.

02. The second advice is that you’d better understand the cause of the problem.