I'd suggest something like Familiam ad sustinendam vivo. Literally translated, this means something like "I live for the sustaining of my family." Latin word order is pretty free, so putting familiam ("family") first emphasizes the importance of that word in the sentence.
This construction (familiam ad sustinendam) is an example of the gerundive, which is a way to turn verbs into adjectives.
You could also say Familiam ut sustineam vivo, which would be using the subjunctive rather than the gerundive. This is an equally correct way of saying it, but using the gerundive adds a flavor of something that must be done that's absent from the subjunctive.
Another way to say it, as @Rafael suggests in the comments, is Pro mea familia vivo, though to my ear Pro familia vivo sounds more idiomatic, the mea ("my") being the sort of thing that Romans tended to assume.
It occurs to me that if what she's looking for is more a motto than a way to make a statement, she might also consider something like Familia mea est vita, which means "My family is my life." (There I'd include the mea because otherwise it would be "family is life, " which seems to be a broader statement about the human importance of family rather than the personal importance of one specific family.)