Hi~ My name is Kim! nice to meet you!
I'm a student and try to improve my English.
(1). As you refered to 2 translation for first sentence, It could be both, in my opinion, but depending on what exactly you want to say. so, If you want to say the causes that make mother's eyes bad is both, it will be first translation you wrote.
However, if you want to say one of the causes that make mother's eyes bad is childbirth, it will be the second one.
However, I read your sentence again. "하고(하다,verb)" is for 임신(pregnant) and 거치면서(거치다,verb) is for 출산의 과정(childbeith). Therefore, I think the second translation will be more proper translation.
I'm sorry for being long explain! ^^;;