There are multiple ways to translate 看在xxx的面子. As a rule of thumb, in order to make a appropriate translation, you should understand the underlying reason why they would "make way" with due regard to somebody else. It can be because:
the person has certain credits, which were accumulated by all the good things he had done previously.
the person is respected/esteemed because of his position, fame, age, seniority and etc.
they don't want the person loses face or they try to save face for the person, because they have built a very good relationship, such as friendship, relatives and etc..
Your sentence '看在你妈妈的面上,我就不为难你(了)', without additional context, can be interpreted as:
Considering/Given the credit of your mother/what those good things your mother have done, I will let you go (this time). // Your mother has credits.
Out of respect for your mother, I will let you go (this time). // I respect your mother because of her age, position, fame, and etc. (most likely the reason without more context)
In order to retain your mother's dignity, I will let you go (this time). // I try to save face for your mother or retain her dignity.
In summary, the interpretation could be various according to the underlying reason given by certain context.
Hope this can help.