someday when my children are old enough to understand the logic motivating a mother,I'll tell them.
I loved you enough to bug you about where you were going and what you would get home.
第一句中logic motivating a mother怎么理解？第二句to bug you about怎么理解？

Someday, when my children are old enough to understand "the logic that motivates a mother", I'LL TELL THEM ........

the logic that motivates a mother 激发一个母亲的逻辑.
意指:一个母亲对孩子的所作所为和良苦用心...

bug 在这里是窃听的意思
I loved you enough to bug you about where you were going,"with whom,and what time "you would be home

我爱你至深才打探你要去何地，跟谁去，什么时候回来。


我找到的英语版本与你的稍有不同:
http://quwstrans.bokee.com/887619.html